Women changing their name at marriage doesn't work well in the modern world. Here's an alternative scheme:
- Women keep their last name at marriage, but change their middle name to their husband's surname. And similarly the man changes his middle name to the wife's surname.
- Children are given the last name of the same sex parent, and start with the middle name of their other parent.
Note that middle name here means the last middle name. Other middle names are also possible though I wouldn't like to see that get out of control.
I did think of having the boys get their mum's lastname, and the girls get their dad's. However looking back to when I was a kid, even though I was closer to my mother, I know I would have wanted to have my dad's surname. I presume that most girls would want to have their mum's name.