I haven't experienced the slightest problem.
I wasn't married to my oldest kids' (twins) father, but he wanted them to have his last name. Everyone thought that was crazy for me to agree to - or even illegal!
> Progressive friends thought, "Why would you GIVE them his name, if YOU'LL be the one raising them?" Well, exactly. There's no question about their connection to ME. If having his name helps HIM feel connected to them, when they're babies and he really has no idea how to care for them...why NOT facilitate that?
> Conservatives (i.e. my parents) thought, "How can you 'pretend' they're not 'bastards', if they ARE?" That seemed so short-sighted. The problem was that we conceived kids together and just didn't know whether WE were going to "work out", long-term. What we NAMED the kids was neither the root of - nor the solution to - that problem.
I do often get called "Mrs. (Ex's-last-name)", by people who know my kids better than they know me. I think that irritates my ex's new wife [who really IS Mrs. (Ex's-last-name)], but she's reasonable about it. It's an understandable mistake. If I expect to form a relationship with someone (like the parent of one of my kids' new friends), I correct them. If it's just somebody passing me in the hall, who knows I'm the twins' mom (and assumes I share their surname), I don't bother to correct them.
Almost without exception, people in a position to check, for example, who's allowed to pick up your kids from school, will KNOW you are their mom and it will never be an issue. In cases where people DON'T know you're Mom, you still will not have a problem. SO MANY kids these days have different last names from one of their parents. It's just not an anomaly, by any stretch of the imagination.
I even have a friend who's married and their kids have different last names from both of them. The husband has a really boring, super-common last name. So the wife kept her maiden name, simply because she liked it. And they invented a last name for the kids, that's a combination of their last names...because they don't like hyphens and double-surnames. And everyone still knows who the kids' parents are.