My partner and I are co-parenting the kids she gave birth to from a previous relationship, but the youngest was only 1 when they separated so her concept of "family" is us. We haven't gotten legally married as our state doesn't allow it, but we had a spiritual union and picked a new last name which our children share, unofficially. At school, they are still mother's legal name and father's legal name hyphenated, but we have a "family" last name for unofficial purposes. Even though their father only sees them occasionally, I still think it would be a slap in the face for them to drop his last name unless they felt strongly about it, so it's not like we would change their last names when we do legally marry, but they have the option to take ours instead.
I know a few couples who just combined their last names when they got married (Brangelina style) or picked a new one, a couple of friends of ours changed it to the place where they met. And others still just picked the last name of the couple who had a supportive family versus the parents who essentially cut them off when they found out they were getting married. I have a hyphenated last name and it's annoying, my parents gave my brother my mother's legal name as his middle name but I got stuck with the hyphenated one because I was a girl, and it does make going about your daily business harder than it needs to be. I'm all about picking a new one.