Can I search for a sitter by name or city?

Unfortunately Rover's search function doesn't have that capability. Sometimes you can find them on Google, using this query string: First Name, Last Name Initial, City, Rover

If not, then you should just call Rover Customer Service at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] and they should be able to find that person for you because they have additional search capabilities.