For me - it wasn't the childrens name that was an issue, but mine was a semi-issue.
I was married for 13ish years. when dh left (he met someone else) the boys were 11 and 5. I had taken ex-dh's name on marriage.
I didn't immediately change my name to ex-dh's on marriage - I changed it for one thing, and then it had a cascade effect, and eventually, I was known as Mrs ex - this was mainly for professional reasons that I didn't change it initially. But the pixwix boys had their dads name. We were married, I had that name eventually, and that was fine.
Ex-dh is a superb dad, and a good ex. - he is very involved in a good way - hands on, takes kids to dentist, combs for nits, buys their presents for school secret santa, and is financially and emotionally supportive in terms of the kids, and although we aren't together, we work as a team.
A year after ex-dh left, Ds1 (then 12) said musingly to me "So are you going to back to your old name now?"
I was a bit taken aback and said "why? how would you feel about having a different name to me, and me going back to my old name - I don't really mind btw" I hadn't really given it that much thought...
Ds1 said he would be cool with it, and was just being curious.
Ds2 then 6, became quite upset, and said he didn't want me to change back, and he wanted me to have the same name as his - I think for him - he'd dealt so well with the whole thing, but having a different name to me, was a tiny step too far, and he needed a small thing as a name to feel more secure for a while.
I felt bad about the boys going through all this, and didn't really much care what name I used - If it made the boys feel better to stick with the status quo at a time of turmoil - that was OK..
When they are older and it isn't an issue anymore, I plan to choose an entirely different name for myself, which is mine - not my dads, and not my husbands - and change to that 