I didn't downvote, but what I really meant is "giving your baby the name 'Baby'".
Btw humans also have many names, depending on context. You might have had funny nicknames in your childhood, your friends speak to you by your first name, other might speak to you by your last name, others might call you "darling" etc... likewise it's also not totally uncommon to speak to babies by the handle "Baby", like "how are you doing Baby?".