can I request a sitters ID?

Of course. While Rover places the responsibility for determining the appropriateness of a sitter in your hands (read their Terms of Service), be assured that it has performed a rudimentary background check.

Once you've met/hired a sitter, there's no reason you can't ask to see an I.D. to ensure that the person entering your home matches the profile. But that's all. You should not expect the sitter to supply you with documentation that includes sensitive identity information.