Would you keep your own surname?

My partner and I are about to get married and he is assuming that I will change my name and our daughters (who has mixed surnames) to his and im reluctant to because of the moral standards associated with his name. His son (whom we have shared care of and love) is the result of a one night stand and was given his surname for reasons that are too long to explain but involves mental stability by his mother. I believe it is husband and wife that should honor the family line of history not a one night stand so will not change mine to it or our childrens as I dont want to be namely associated with that kind of history. My partner has suggested to have his sons name changed to his and his mothers so me and our kids are named who we really will be. What do you think?