In practice, you can just keep using your maiden name if you wish, or you can use your married name. Your marriage certificate and birth certificate are usually
all the cross reference evidence you need.
It need not really be a problem.

People use lots of different names at different times in their lives.
However problems can happen when your name is not consistent with important documents especially those commonly used as ID.
Organisations are asking more and more for ID and the least amount of confusion the better.
A 'Mix & Match' approach will inevitably become a headache.