You absolutely can keep your married name once you get divorced. Put more
simply, names remain the same if you don't take affirmative steps
to change them.
When you first married and filled out a marriage license application, you
needed to take affirmative steps to change your last name. Without specifically
requesting a name change on the application or in a separate request later
on, your name remains the same.
Similarly, you need to take affirmative steps after divorce if you want
to change your name. Otherwise, you can keep your married name as long
as you want. If at some point you want to change your name after divorce,
you would need to do so through the superior court of the county you reside
in by making an ex-parte request.
§§ 2080-2082; see also
California Code of Civil Procedure
§ 1276(a). This will restore your birth name or former name. If you
do not complete these steps your married name will remain the same.