I can see the "name matching" thing. I also have an issue with the child's names being different than the mother's (if that's who they live with). One of the reasons WHY was b/c I was concerned how my daughter would feel growing up, having a different last name.
So I'm really really glad, AH, that you shared your own daughter's feelings on the matter.. reaffirmed what I feared for my own.
Since stbx and I were married SUCH a brief period of time and given our daughter's age, I petitioned, as part of the divorce to change her last name on her birth certificate to a hyphenated form of BOTH of our last names; however, she will "go by" my maiden name, which is what I will be returning to once the decree is issued.
I did have an issue with his first wife keeping his last name... but not b/c of her per se, or his other daughter, but b/c she was having ANOTHER child, by someone else, who was legally still married.. I had a concern that since her last name was my stbx's last name that she'd try to give THAT last name to the new child. THAT would be a no-no, wouldn't it? I mean, I guess it's "legal" but morally that'd just be super super super tacky no?
She ended up returning to her maiden name anyway, we have no idea what the other kid's last name is.. presumably her maiden name.
The best we can do is live our lives with enlightened improvisation.