Here the word "it" refers to any miracles or teaching Peter and John might continue to do. Alternate translation: "in order that news of this miracle spreads no further" or "in order that no more people hear about this miracle" (See: [[rc://en/ta/man/jit/figs-explicit]])
Here the word "name" refers to the person of Jesus. Alternate translation: "not to speak anymore to anyone about this person, Jesus" (See: [[rc://en/ta/man/jit/figs-metonymy]])