My wife's first name and my last name would sound really awkward together, which is the main reason why she kept hers and why it never bothered me that she did.
It is annoying to have to explain to people at places like hospitals that we're married even though we have different last names.
Yeah, that is definitely another time when it's been a pain. Picking up a kid from daycare or school.
My daughter shares my last name, so when my wife came to pick her up, I sometimes got a phone call. Even if we filled out a form putting both of our names on it.
My wife kept her name (both of our names are important to us, and neither of us care about tradition). So far no real issues, just people who know one of us assuming the other shares a last name. Unless it's someone we're going to interact with a lot or we're filling out paperwork, we don't bother correcting them.
We are trying to have a kid, and if we succeed we'll give them her last name. So... I'm super looking forward to being a man picking up a kid with a different last name and all the assumptions I'm probably going to have to face. I'm just hoping by the time that happens this will be a normal enough occurrence that it won't be a big deal.