If I was to open a Dog Walking / House Sitting company under my name and keep Rover strictly for Boarding / Day Care would I need to remove Dog Walking and House Sitting from my profile. What would be the correct and fair way to run these services?

You are an independent contractor. You are under no obligation to provide exclusive services for Rover. So long as you do not poach clients from the Rover platform, then you are fine. Many Rover sitters and walkers may also be listed by other companies, like Wag. So your situation isn't unique. I board dogs outside of Rover and feel no need to convert those clients to Rover.

Karen's answer is correct. If the client finds you through Rover platform, they need to be booked on Rover for whatever service is needed. If the client finds you through referral or some other source, you can simply book the service on our own.

Other comments answered what you shouldn't do...take Rover clients off the platform. If you found them through Rover, you are obligated to use Rover for them, part of the Terms of Service you agreed to when you joined Rover.

I wanted to add that since you're planning to expand your business, your best interests are to offer as many services on Rover AND privately. Less options=less opportunities for clients. Use Rover to its full potential while building up your private business!