Good grief. Girlfriend is lying to you op.
firstly that’s not how sperm donors work, she’s fallen pregnant to a guy she was seeing, he’s not wanted to be with her, she’s had the baby anyway, so he’s now wishing to be involved as she did proceed and have the child. the woman isn’t being honest with you.
She’s lying through her teeth.
He isn’t a donor, even though it suits her to pretend he was, he is a man she had a brief sexual relationship with, she wanted more, he didn’t, she fell pregnant, he didn’t want the kid or her to have it, she proceeded and now the child is here he is stepping up. The fact he even went to court to get access and on the birth certificate shows the likely hood of him being some weird donor you shagged as incredibly low. Sperm donors provide a cup of semen. They don’t have repeated sex with you till you conceive and have discussions on a relationship.
and no, you can’t just change a kids name, both parents have equal rights, she can no more do it than he can. They are equal parents in thr eyes of the law irrelevant of the custody arrangements.