My mum changed hers when she divorced my dad (not when they separated). She didn't change ours as she divorced dad, we didn't. And it would have been a little unfair for him for us to lose his surname.
My MIL has been separated for 22 or so years, and still has her married name. She will never divorce FIL, so will always keep the name.

Personal choice I think. You need to do what you feel comfortable doing.