To be honest Melly, I'd be giving the baby your name to avoid issues in later life for the child and yourself with regards to identity. If you put the fathers' name on the birth registration and decide to remove it later for any reason, it can be very difficult. Especially if the father is likely to create problems for you.
And it isn't my call and I have no right to stick my nose into your business, but if the father of the baby is going to be so silly and childish, perhaps you're much better off without him anyway.

Lisa