It is implied that the Jewish Christians were the ones who would baptize them. Alternate translation: "Peter commanded the Gentile believers to allow the Jewish Christians to baptize them" or "Peter commanded the Jewish Christians to baptize them" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/figs-activepassive]])
Here "in the name of Jesus Christ" expresses that the reason for their baptism was that they believed in Jesus. Alternate translation: "be baptized as believers in Jesus Christ" (See: [[rc://en/ta/man/translate/figs-metonymy]])