I did change my name to my husbands. In America it is common. Being my last name was Dell (ex-husband) I was very happy to change it to my current husband. Before that my last name was that of my step father who legally adopted me at age 9; it was even changed on my birth certificate
I am not sure how I feel about not having my husbands name. I actually love it. I guess because normally, if a mother has a different name than the child, some just automatically think you are not married or the child is out of wedlock (In this society). Allah is all knowing, he knows who my father is, I know who my father is. Maybe I just don't understand the big deal.
Tidbit: In ancient times some used to follow Matrilineality (mothers lineage). The reason for this was you always knew who the mother was but could not guarantee who the father was. Can you imagine that! OMG.