I HAVE MILTIPLE PEOPLE ASKING ME TO DOG SIT FOR THEM AND I WANT THEM TO GO THROUGH http://ROVER.COM TO BOOK IT BUT I CANT FIGURE OUT HOW THEY CAN SPECIFICALLY FIND ME
No, there is no way to search by name.
Instead, go to your Dashboard and create a promo code that will give first-time Rover customers $20 off their first booking. It doesn't come out of your pay. When you have the have the promo code, there will be a unique url created that you can give those friends.
I see that your Profile is not yet active. You will have to wait until it has been approved by Rover before you can give out the info to those people. You can also get business cards through Rover with your url/code on them.