J.F.
I know your question isn't "Should I have baby's last name be the same as mine or the daddy's?" but, can your mom make that choice.
No, your mom can't make that choice, BUT I want to share a story with you. I've been a close "older sister/mom" mentor of a young lady for the past several years. I knew her when she was 13 and when she became pregnant at 16. She is now turning 19 in Jan. and baby girl will be 3 in Dec. She wanted the daddy's name on the birth certificate because he WAS stepping up to the plate at the time of her pregnancy. He even stayed in the picture for the entire first year. A few months after that she was going to move in with him and they were going to have their own apartment. Things didn't go well. They separated by her choice. He got a new girlfriend and she moved in with him. He and the girlfriend didn't do the best job taking care of the little girl while in his care. When the little girl was just over 2 years of age they were in the court battling over custody (he didn't want to pay child support, didn't care that the girl had a food allergy, and smoked around her). She won custody and daddy barely cares to see the girl now. This teenage mom now REGRETS having the girl have her last name. (I know you are thinking, "Well that happened to that girl and won't happen to me." but it happens many more times than you would like to admit.)
I KNOW you think this will work out and you all will live happily after. I hope you do!!!! But, please take this old lady's advice and advocate for your child's well being right now. You can always change your child's name when the two of you marry and you change your name. Consider it a "two-fer" :)
It is MUCH easier (and cheaper) to change a name in a positive direction than a negative one.
I wish you all the best. I'm glad you found MP. It helped me a lot when I was a first time mom. :)