Why didn’t the disciples baptize using a Trinitarian formula as commanded in the Great Commission? If the Mathew 28:19 (and the Great Commission therein) is considered an authentic verse, why aren’t there any instances in the NT where the apostles actually baptized someone using the Trinitarian formula (i.e., “in the name of Father, and of the Son, and of the Holy Spirit”)?


  19 “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, NKJV, 1982


I'm looking for explanations given by defenders of trinitarianism.
In Acts (2:38, 8:12, 8:16, 10:48, and 19:5), baptism "in the name of the Lord Jesus" is mentioned. By saying "name" (singular), the Divine Essence of the Holy Trinity is signified, not the Persons individually. It is not not solely the Second Person of the Holy Trinity who effects baptism, but all the Persons working together as one.

As the Catechism of the Council of Trent §The Sacrament of Baptism, says regarding the form of the sacrament of baptism,


  Baptism is the work not of the Son alone, of whom St. John says, He it is that baptizeth (John 1:33), but of the Three Persons of the Blessed Trinity together. By saying, however, in the name [singular], not in the names [plural], we distinctly declare that in the Trinity there is but one Nature and Godhead. The word name is here referred not to the Persons, but to the Divine Essence, virtue and power, which are one and the same in Three Persons.


Also, see these sections of idem:


  Essential And Non­-Essential Words Of The Form
  
  It is, however, to be observed that of the words contained in this
  form, which we have shown to be the complete and perfect one, some are
  absolutely necessary, so that the omission of them renders the valid
  administration of the Sacrament impossible; while others on the
  contrary, are not so essential as to affect its validity.
  
  Of the latter kind is the word ego (I), the force of which is
  included in the word baptizo (I baptise). Nay more, the Greek
  Church, adopting a different manner of expressing the form, and being
  of opinion that it is unnecessary to make mention of the minister,
  omits the pronoun altogether. The form universally used in the Greek
  Church is: Let this servant of Christ be baptised in the name of the
  Father, and of the Son, and of the Holy Ghost. It appears, however,
  from the decision and definition of the Council of Florence, that
  those who use this form administer the Sacraments validly, because the
  words sufficiently express what is essential to the validity of
  Baptism, that is, the ablution which then takes place.
  
  Baptism In The Name Of Christ
  
  If at any time the Apostles baptised in the name of the Lord Jesus
  Christ only, we can be sure they did so by the inspiration of the Holy
  Ghost, in order, in the infancy of the Church, to render their
  preaching more illustrious by the name of Jesus Christ, and to
  proclaim more effectually His divine and infinite power. If, however,
  we examine the matter more closely, we shall find that such a form
  omits nothing which the Saviour Himself commands to be observed; for
  he who mentions Jesus Christ implies the Person of the Father, by
  whom, and that of the Holy Ghost, in whom, He was anointed.
  
  And yet, the use of this form by the Apostles seems rather doubtful if
  we accept the opinions of Ambrose and Basil, holy Fathers eminent for
  sanctity and authority, who interpret baptism in the name of Jesus
  Christ to mean the Baptism instituted by Christ our Lord, as
  distinguished from that of John, and who say that the Apostles did not
  depart from the ordinary and usual form which comprises the distinct
  names of the Three Persons. Paul also, in his Epistle to the
  Galatians, seems to have expressed himself in a similar manner, when
  he says: As many of you as have been baptised in Christ, have put on
  Christ, meaning that they were baptised in the faith of Christ, but
  with no other form than that which the same Saviour our Lord had
  commanded to be observed.