To me, names are about connections with people. Either the connection to your parents who named you as a baby, the connection to your friends or special someone who have given you a nickname of some sort, or the connection to the family you chose/created when you got married or had kids together.
Currently, the name I have is one that I love and treasure. Even the last name which is mine only due to marriage I love. However, the reasons I love my last name have nothing to do with who I got it from anymore. The reasons I love it are cute, small, and snuggling with me as I type this. C and R have that last name and it is a connection we share that I love to be able to point to and say, "See, they're mine."
A few days ago I was told by the STBE, their father, that when the divorce is final I have to change my last name back to my maiden name. I told him he was crazy. Yep you read that right, I fully intend on keeping the STBE's last name. But its not because I want to keep a connection to him, its because I don't want to remove the one I have to the kids. His argument? I gave birth to them so I will always have a biological connection to them so I don't need to have the same last name as them just like he didn't have the same last name as his mom when he was growing up.
Well the reason his mother didn't share his last name was that she had remarried. If the day comes that I do get remarried its entirely possible that at that time I'll want to take a different last name, especially if the person I'm marrying wants me to. Until then I want to keep the same one that my children have. Maybe its not the typical way of doing things for most divorcing couples, and maybe he's going to resent me for keeping a name that he says I have no right to anymore, but for now its how things are going to be and the STBE is just going to have to deal with it.