Whether you keep your name depends on when you got married. Back in the 1960s I wanted to keep my name and investigated it as well as I could.
I was told, erroneously, that, legally, I had to have my married name on my passport and that it could cause problems and confusion doing anything as a married couple (mortgages etc) if we had diferent surnames.
In the end the problems seemed so insurmountable I gave up and went along with changing my name. Although i always thought that if my marriaage ever ended, and it hasn't, I would immediately revert to my birth name.