Although the Greek of this sentence merely has “he,” Good News Translation introduces the name Jesus, since a new section begins here

In him is literally “in his name”; see comments at 14.13.

As in most contexts in the Gospel of John, believed in him must be understood in the sense of “trusted him” or “put their faith in him.” It means more than merely believing what he said or giving assent to his message. There is always the implication of confidence, loyalty, and trust.

Miracles is the same word discussed in 2.11. In speaking of “performing miracles” one must use an expression which is natural in the receptor language. This may differ from language to language, for example, “the miracles which he caused to happen,” “the wonderful deeds which he did” or “the revealing great things which he made.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on the Gospel of John. (UBS Handbook Series). New York: UBS, 1980. For this and other handbooks for translators see here .