Speaking from experience, sometimes you can not particularly like your surname, and then come face to face with the possibility of changing it and realise that it would be weird to change it, because like it or not, it is your name and your identity. I always assumed I would change my name upon marriage, and then I just never did, because it felt weird. I think the older the woman is at the time, the more likely she is to feel weird about changing her name. Because she's been living with it for much longer, and she's also had more time to consider how sexist this tradition actually is.
The point is, she doesn't have to compromise. It is her decision and hers alone. And the more he tries to throw his weight around, the more she will dig her heels in.
Tell me this. If they were married and he actually had a say in this, do you think he would be proactively suggesting a double barrelled surname? Or would he be perfectly happy for the baby to just have his surname? Because when you talk about compromising, it kind of suggests that he and his friends think the default position is that the baby ONLY has their father's surname, and that double barrelling is something to be reluctantly agreed to if the missus really insists.
Why does he think it would be perfectly fine for the woman who has literally grown this child in her body and given birth to it and will most likely be the primary caregiver to not have her identity represented in her child's name AT ALL, whereas the man who did nothing but ejaculate (and then ask a 40 year old woman to have an abortion because he wasn't ready yet) gets to pass on his surname and his alone?
Honestly, the sheer entitlement of these men.
She is absolutely right to dig her heels in, and more women should do likewise. In her position I wouldn't want to double barrel either. I would take the view that he had done nothing to deserve any compromise from me, and that this man-child who wanted me to terminate what might be my only successful pregnancy because at the age of 40 he doesn't think he's good enough at adulting to be ready for fatherhood yet was unlikely to be a good father or stick around for the long haul. Fathers who prove their worth can be married or added to birth certificates and given parental responsibility later. Children's names can be changed or double-barrelled at a later date with the consent of both parents. But deadbeat dads who want all the perks of fatherhood without any of the responsibility can be a thorn in your side until your child has reached adulthood.
He has one job now, which is to prove to her that he is actually willing to commit to her and their child, and to be a good dad. So he needs to stop moaning about the name and get on with it.