My question is i thought i was doing the right thing by giving my name to a baby that ain't mine how do i correct my mistake?

Would a biood test be done at that time to change the baby name and take my back?

That's along process that will not be done in same room will be done in another youbwill have to petition the other parent to court then you will need a DNA test all depends on that if a judge will remove the name a judge will not remove a name or a parent's name from a birth certificate just because somone says I'm not the parent ,court days ahead with alot of cost good luck

You have a process on your hands and a few hundred of dollars. A judge would need to order the change of name for the child in question you will also need to undergo a DNA test to prove paternity. Do some google searches on the whole process