How much and can I change my baby's middle name

I don't exactly understand your question. Can you clarify it please? Do you want to change the spelling? The whole name? Please ask your question so it is easier to answer, because it is very unclear what you want to do.

Depending on where you live, if you want to change the name on the birth certificate, you would have to apply to do that. Where I live you have to do that at the court house, and just ask for a change of name application, and then submit it. There may be other steps, and a fee, but you can legally change your name, pending approval.