Because that for his name’s sake - The word “his” here refers to God; and the idea is, that they had undertaken this journey not on their own account, but in the cause of religion.
They went forth - Or, “they have gone forth” - ἐξῆλθον exēlthon - referring to the journey which they had then undertaken; not to the former one.
Taking nothing of the Gentiles - The term “Gentile” embraced all who were not “Jews,” and it is evident that these persons went forth particularly to labor among the pagan. When they went, they resolved, it seems, to receive no part of their support from them, but to depend upon the aid of their Christian brethren, and, hence, they were at first commended to the church of which Gaius and Diotrephes were members, and on this second excursion were commended particularly to Gaius. Why they, resolved to take nothing of the Gentiles is not stated, but it was doubtless from prudential considerations, lest it should hinder their success among them, and expose them to the charge of being actuated by a mercenary spirit. There were circumstances in the early propagation of Christianity which made it proper, in order to avoid this reproach, to preach the gospel “without charge,” those to whom it is preached to contribute to its maintenance, and that it is the right of those who preach to expect and receive a support. On this subject, see the 1 Corinthians 9 notes, particularly 1Jo 1:15, 1Jo 1:18 notes.