The name of the Lord Jesus
(to onoma ton kuriou Ihsou
). Apollos was not rebaptized. The twelve apostles were not rebaptized. Jesus received no other baptism than that of John. The point here is simply that these twelve men were grossly ignorant of the meaning of John's baptism as regards repentance, the Messiahship of Jesus, the Holy Spirit. Hence Paul had them baptized, not so much again, as really baptized this time, in the name or on the authority of the Lord Jesus as he had himself commanded ( Matthew 28:19
) and as was the universal apostolic custom. Proper understanding of "Jesus" involved all the rest including the Trinity (Father, Son, and Holy Spirit). Luke does not give a formula, but simply explains that now these men had a proper object of faith (Jesus) and were now really baptized.