I would like to keep my surname as well as take the man's, mainly because I see it as a sign of ownership, as though the man has full rights of the woman because she's not even allowed to keep a part of herself she was born with. I also like my surname, even though nobody can pronounce/spell it.
When I get married, I also don't want to be pronounced as 'man and wife'. I do not belong to a man. He is my HUSBAND and I am his WIFE. There, now that's equal.
I might seem a bit pedantic here but I have a very dour view of this tradition. Marriage is for both people involved.
Anyway enough of that lol.
To answer Sydney's question, I don't see why the kids can't take both names. They came from both parents. If the father only wanted them to share his name, then yes I would say it was a lack of unity, unless the woman agrees to it.