Of course 1000% you are not being unreasonable. AT ALL. EVER. end of!
Babies are people and people are not there to remind us of loss, or love, family, or friends, or other special people.
"She told me she hates DDs name"
That's a shame sis, but that is her name.
"and is upset that it isn't our mum's name."
It's sad that you are upset but you know, of course, she is my baby, with dp/dh and we get to name her.
"I said I didn't think it suited DD but I was sorry she was upset. I also mentioned that at least this way it leaves my mum's name for my sister to use if she has kids."
You don't need to explain whether name suits baby or not, I mean, of course, you can, and you did, but really, your baby, your choice of name.
"My sister said that it wasn't good enough she was really upset about it."
Tough Titty, as they say! Really it is a shame because now she is an auntie, and aunties are very special people who get to play a special part in the lives of kids, if they can be arsed to do so!
"She doesn't want to use mum's name and she probably won't have kids anyway so she wanted me to carry on the name."
But she doesn't get to decide that for you.
"She then told me that I had really hurt her and we couldn't recover from this. Then DD wanted feeding and she sighed and said she was leaving."
Sorry, OP but either your sister is majorly melodramatic or mentally ill. I am not at all being flippant. I really think you need to pass this issue on to your dad and let other family members deal with it.
DO NO allow your sister to spoil this special time.
"She has agreed to come and visit tomorrow to talk about it more." How big of her. Please do not spend too long on this. Tel her you love her, she'll always be your little sis and you will always be her big sis.
She is either someone who is very selfish and manipulative or she needs to see a counselor for unresolved grief. Maybe a bit of both.
"I don't know how to explain it to her. I don't want DD to have mum's name but sister is so upset and I feel so guilty because I have upset her."
YOU have not upset her, she is either playing up or dealing with her own internal demons. Speak to your dad, step mum or aunt and explain simply that your sister does not get to name your baby.
Do not allow this to take up to much time. You need to bond with your baby, others can deal with this drama.