question: Why is it a son named after his father is a “Jr.” but a daughter named after her mother not?
comment: From a genealogist's perspective, "Jr" wasn't historically a part of a name. In small towns it wasn't unusual for two men to end up with the same name. Sometimes they were related father/son, grandfather/grandson, uncle/nephew or sometimes, it was coincidental and there was no relation at all. To distinguish themselves in newspapers, property records, etc, they would usually apply 'Jr' to the younger one. 'Sr' was used far less often for whatever reason. Women, conversely, were usually referred to as "Mrs Husband's name" in newspapers and other records, and very rarely were allowed to own property on their own, so no distinguishing Sr or Jr were needed.
passages: Naming a child after a relative, friend, or well-known person is a common practice in the English-speaking world. When a son is named for his father, it is customary (primarily in the United States) to add "Jr."/"II", "III'", or another name suffix to the name of the son (and sometimes "Sr." or a prior number to the father's name), in order to distinguish between individuals, especially if both father and son become famous, as in the case of poet Oliver Wendell Holmes Sr. and his son, Oliver Wendell Holmes Jr., an Associate Justice of the United States Supreme Court. Sometimes the "Jr." or "Sr." suffix is applied even when the child's legal name differs from that of the parent. 
   Section::::Unusual naming variants.
   Mrs. Cheney's mother, Mrs. Ednah P. Littlehale, a native of Exeter, New Hampshire, born in 1799, died in Boston in 1876. She was the daughter of Jeremiah and Ednah (Parker) Dow and on the paternal side a descendant in the seventh generation of Thomas Dow, one of the early settlers of Newbury, Massachusetts, freeman in 1642. The Dow ancestral line is Thomas, Stephen, Nathaniel, Captain Jeremiah, Jeremiah, Ednah Parker (Mrs. Littlehale).
   Although there are instances of daughters being named after their mothers and also using the suffix "Jr." (such as Anna Eleanor Roosevelt Jr., Winifred Sackville Stoner Jr., and Carolina Herrera Jr.), or after their grandmothers or aunts with the suffix "II", this is not common. Usually, the namesake is given a different middle name and so would not need a suffix for differentiation. Furthermore, once the woman marries, she would most commonly take the surname of her husband and thus do away with the generational suffix. The title "Jr." is sometimes used in legal documents, particularly those pertaining to wills and estates, to distinguish among female family members of the same name.
   Some confusion has been generated by the fact that Andrew Gordon is usually referred to by his surname. Regarding this, he has said, "I know it can be confusing, but here is the deal: My legal or if you prefer, government name, is Andrew Beauregard Gordon. Andrews is my grandmother Helen’s maiden name and my middle name comes from the confederate general PGT Beauregard who fired on Fort Sumter and basically started our Civil War. Ilona calls me Gordon and that is how I think of myself, in the military we always used our last names."
   Martha Livermore, wife of Abraham Parker, of East Bradford, was a daughter of John Livermore, of Watertown, Massachusetts (the founder of the family of this name in New England), and his wife Grace (born Sherman), whom he married in England, and who was closely related to the immigrant progenitors of the most prominent Sherman families of America. Mrs. Grace Sherman Livermore was a useful member of the colony, being an obstetrician. She survived her husband, and died in Chelmsford in 1690, aged seventy-five years (gravestone). Judging from printed records, the name Ednah has come down to Cheney not only from her mother, her grandmother Dow, and her great-grandmother Parker, but from a more remote ancestress, Mrs. Ednah Bailey, wife of Richard' Bailey, of Rowley, Massachusetts. Tracing backward, Mrs. Ednah Hardy Parker, born in 1745, was the daughter of Captain Eliphalet and Hannah (Platts) Hardy, granddaughter of Jonas Platts and his wife, Anne Bailey, and great-grand-daughter of Deacon Joseph Bailey, of East Bradford, who was son of Richard and his wife Ednah. Richard Bailey was one of the company that set up in Rowley the first cloth-mill in America. Mrs. Ednah Bailey's maiden name is thought to have been Halstead.
   One easily understandable example of retroactive nomenclature is the tradition in many countries that a woman adopts the surname of the man she marries while remembering her "maiden name" as the way she was referred to her pre-marital days. Radio talk-show host Michael Medved once made the statement: "Hillary Clinton used to be conservative when I knew her in our college days." But in Hillary Rodham's college days she was not yet married to Bill Clinton; therefore there was no "Hillary Clinton" at that time. However, in such a case as this it is easily understood that he meant the woman who later became known as Hillary Clinton.
   Some Vietnamese names also function this way, as less of a "tradition" than a style or trend, in which the mother's maiden name is the child's middle name.
  
  Section::::Europe.
  
  Section::::Europe.:England.
   BULLET::::- John Rodgers Meigs (1842–1864), a West Point graduate and Army officer who was killed in action during the Civil War
  
  BULLET::::- Mary Montgomery Meigs (1843–1930), the wife of Army officer Joseph Hancock Taylor, who was the son of Union Army Brigadier General Joseph Pannell Taylor, and nephew of President Zachary Taylor
  
  BULLET::::- Charles Delucena Meigs (1845–1853), who was named for Meigs' father
  
  BULLET::::- Montgomery Meigs (1847–1931), a civil engineer who enjoyed a long career in railroad, bridge, canal, power plant, and road construction
  
  BULLET::::- Vincent Trowbridge Meigs (1851–1853)
   Several names have been used at various points during Clinton's life, including names preferred by Clinton, names used for her by political opponents, and names used for her by others. Following her birth at Edgewater Hospital in Chicago, Illinois, Clinton was initially named "Hillary Diane Rodham", and was generally referred to as "Hillary Rodham". In some formal settings, she used "Hillary D. Rodham", which appeared on her senior thesis, in the transcript of her Wellesley graduation speech, in reports of the United States House of Representatives investigation into the Watergate scandal, and as chair of the Legal Services Corporation. In 1995, Hillary Clinton said her mother had named her after Sir Edmund Hillary, co-first mountaineer to scale Mount Everest, and that was the reason for the less-common "two L's" spelling of her name. However, the first successful Everest climb did not take place until 1953, more than five years after she was born. In October 2006, a Clinton spokeswoman said she was not named after the mountain climber. Instead, this account of her name's origin "was a sweet family story her mother shared to inspire greatness in her daughter, to great results I might add."
   After her death, Sara Agnes Rice Pryor was buried at Princeton Cemetery, near her sons Theodorick and William. Her husband was also buried there after his death. Her daughter Mary Blair Pryor Walker was also buried there after her death. 
  
  Sara Agnes Rice Pryor's influence on the matrilineal naming for Mary Blair is documented in her great-great-great-granddaughter's book, Mary Blair Destiny published in 2019. 
  
  Section::::Works.
  
  All published in New York by Macmillan:
  
  BULLET::::- "The Mother of Washington and her Times", New York: Macmillan Company, (1903), available as free e-book at Googlebooks
   In Season One's "What's in a Middle Name?" episode of "The Dick Van Dyke Show", (1961-1965), characters Sally Rogers and Buddy Sorrell have an animated discussion of baby names, as follows:
  
  Buddy: "I got it! I got it!"
  
  Sally: "What is it?"
  
  Buddy: "Humphrey!"
  
  Sally: "Get rid of it!"
  
  Buddy: "What's the matter with Humphrey? Bogart didn't do bad with it."
  
  Sally: "Well, Maria Ouspenskaya didn't do bad either, but would you name YOUR kid Maria Ouspenskaya?!"
  
  Buddy: "No, and for only one reason."
  
  Sally: "Why?"
  
  Buddy: "Because my brother named HIS kid that!"
   "Jr." or "II" can be used when being named after the father, however they are both pronounced differently; "Jr." is pronounced as "junior" and "II" is pronounced as "the second". Roman numeral suffixes can be used to name after other family members like an uncle, cousin, or ancestor (including grandfather). The suffix "III" is used after either "Jr" or "II" and, like subsequent numeric suffixes, does not need to be restricted to one family line. For example, if Randall and Patrick Dudley are brothers and if Randall has a son before Patrick, he will call his son "Patrick II". If Patrick now has a son, his son is "Patrick Jr." or "Patrick II" if Randall doesn't have a son named Patrick II. As time passes, the "III" suffix goes to the son of either Patrick Jr or Patrick II, whoever is first to have a son named Patrick. This is one way it is possible and correct for a Junior to father a IV. Another example involves President Ulysses S. Grant and his sons Frederick, Ulysses Jr., and Jesse. When Frederick's son Ulysses was born in 1881, Ulysses Jr did not yet have a son named after himself. Therefore, Frederick's son was Ulysses III. Ulysses Jr's son, born afterwards in 1893, was Ulysses IV. Jesse's son Chapman was the father of Ulysses V, as neither Ulysses III nor Ulysses IV had sons named for themselves.
   Blair Niles was the grand-daughter of Sara Rice Pryor and Roger Pryor, and the daughter of Marie Gordon Pryor. Her unique namesake, "Mary Blair," is shared with her mother's sister, Mary Blair Pryor, her cousin Mary Blair Walker Zimmer, and several other women in her lineage, as documented in *"Mary Blair Destiny". Her grandmother Sara Rice Pryor was also a widely-read author for her chronicling of life in antebellum Virginia. Blair Niles did not have any children of her own.
   When Jeffrey and Prudence's first baby was a boy, they named him Hazard. He would father nine children and live to the age of 72. When Hazard was 2½, a baby sister was born. I like to think it was her mother who gave her the name Delight in honor of her lost sister—not Jeffrey naming his daughter after his first wife. Three and a half years later, in November 1802, twins George and Allis joined the family.[3] A brother John was born in 1808.
  
  We have the following account from Bob Champlin about Jeffrey:
   BULLET::::- Julia Maria Ridgely (b. 1841)
   BULLET::::- -aei (Persian) (See -i) for words that end in the long vowel "A"
  
  BULLET::::- -ago (Russian) (e.g. Zhivago)
  
  BULLET::::- -aitis (Lithuanian) "son of"
  
  BULLET::::- -aitė (Lithuanian) signifies an unmarried female
  
  BULLET::::- -aty Americanized form
   The late Senator Robert Kerr of Oklahoma once quoted Chauncey Depew in an attack on a Senator from Indiana, "As I gaze on the ample figure of my friend from Indiana, and as I listen to him," Kerr began, "I am reminded of Chauncey Depew who said to the equally obese William Howard Taft at a dinner before the latter became President, 'I hope, if it is a girl, Mr. Taft will name it for his charming wife.' "To which Taft responded, 'if it is a girl, I shall, of course, name it for my lovely helpmate of many years. And if it is a boy, I shall claim the father's prerogative and name it Junior. But if, as I suspect, it is only a bag of wind, I shall name it Chauncey Depew.'"
   BULLET::::- A woman could also be named for her father's family and a place of origin (somewhat like men, but without a unique praenomen). For example, in the Robert Graves novel "I, Claudius", Caligula's sister Julia Livilla is named Lesbia, reflecting her birthplace, Lesbos.
   This information, though, is not present in recent, solid historical books about Nancy Hanks. Perhaps a sign that the Berrys did not consider Nancy a daughter, in Richard Berry's will he mentions a daughter Sarah [Mitchell], but not Nancy.
   BULLET::::- A woman could be named for a grandparent. For example, Livilla, sister of Germanicus and Claudius, was named for her paternal grandmother Livia.
  
  BULLET::::- A combination of her family name and the name of a mother or grandmother. Claudius's first wife Plautia Urgulanilla was named for her father's family, Plautii, and her paternal grandmother Urgulania, a close friend of Claudius's own paternal grandmother Livia.
   BULLET::::- "Lady Penelope Pryer:" Lady Penelope Pryer is an upper-class woman who disapproves of the Bradfords when they arrive in Bath. She does take a liking to Julia because she is able to shape her into a proper woman. The novel ends with a recap of Lady Pryer's engagement to Gregory Leadenhead.
  
  BULLET::::- "Gregory Leadenhead:" Gregory Leadenhead was briefly married to Julia, but once he found out about her affairs he demanded a divorce.
   BULLET::::- O'Hara Boys: are the three boys of Ellen and Gerald O'Hara who died in infancy and are buried 100 yards from the house. Each was named Gerald after the father; they died in succession. The headstone of each boy is inscribed "Gerald O'Hara, Jr." (It was typical of families to name the next living child after the parental namesake, even if a child had already died of that name.)
   BULLET::::- The written style of address of the heir to a laird is (for example) "John Smith of Edinburgh, Younger" or if abbreviated "John Smith of Edinburgh, Yr." or in the case of the heir to a chief "James Salmond of that Ilk, Yr." or "James Salmond of Salmond, Yr."
  
  BULLET::::- If a female is the heir in her own right, then she is styled in the same way as a male.
   It was conferred to:
  
  BULLET::::- First class: mothers bearing and raising nine children.
  
  BULLET::::- Second class: mothers bearing and raising eight children.
  
  BULLET::::- Third class: mothers bearing and raising seven children.
  