Possible meanings are 1) this is the reason the man was made strong. Alternate translation: "Because of faith in his name" or 2) this is how the man was made strong. Alternate translation: "By faith in his name"
The word "his" refers to the Founder of life, Jesus. The abstract noun "faith" can be translated with the verb "believe." Possible meanings are 1) the lame man had faith in Jesus. Alternate translation: "Because he believed in Jesus name" or 2) Peter and John, and perhaps the lame man, had faith in Jesus. Alternate translation: "Because we believed in Jesus' name" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
# his name
The phrase "his name" is a metonym either for Jesus or for Jesus' power. (See: [[rc://en/ta/man/translate/figs-metonymy]])