The Bible says a man and woman should cleave together as one. If God says a man should leave his home and cleave to the wife, same then applies to the woman. Some women say they have made a name in their career and wouldn’t want their names to be mixed up with that of another, so they add their maiden names. Some also have parents who are rich or influential and by still using their parents’ names they believe doors would be opened unto them.
I believe this is not necessary. Whatever name you have made or feat you have performed in your career or profession or the family you are from, since you have made up your mind to marry your spouse, then you have agreed to sign off your maiden name and take up your spouse’s name. Holding on to your maiden name is to say you are still holding on to your father’s home.