What is the ruling on naming a boy with two names at the same time? Is that considered an innovation (bid'ah)? And what is recommended for a son to be named?

There is no harm in naming a newborn with two names, and this is not an innovation (bid'ah), because these are worldly matters not intended as acts of worship. Just as it is permissible to name a child with a single name, a kunya (patronymic/matronymic), and a laqab (nickname), this was common during the eras of the Companions and those who came after them, and it involves honoring and showing affection to the child.