Is it necessary to take your husband's last name?

I did not take my husband's last name - although our children have his name. Normally, neither my husband nor I have any issues with this arrangement. However, recently I was talking to a girl friend who had just gotten married and changed her name and she was shocked that I had kept my name. Shocked! 

Her arguments were:

1. This will confuse your kids

2. If you cannot agree on a last name, how can you hope to agree on anything else?

3. It's sexist no matter what. Your last name is your father's last name - so what does it matter if you change it to your husband's last name? 

What do you think?