Ruth 'the wife of Mahlon' or Elimelech? Why is Ruth called 'the wife of Mahlon' (Ruth 4:10) whereas in the beginning of the story she is the wife of Elimelech?
You are mistaken:


  The man’s name was Elimelek, his wife’s name was Naomi, and the names of his two sons were Mahlon and Kilion...They married Moabite women, one named Orpah and the other Ruth. - Ruth 1:2,4 NIV [Emphasis added]


So it is Naomi, not Ruth who was the wife of Elimelech; the verse you cited gives the more specific information that Ruth married Mahlon whereas chapter 1 leaves it open as to whether it was Mahlon or Kilion that she'd married.