How about taking the name of a famous local landmark, state park, etc and adding "pet resort" to it. For instance, if you are located near Washington, DC - The Capital Pet Resort & Spa or The White House Pet Resort & Spa. There is a nice pet resort in IL called the "Starved Rock Pet Resort", because of it's near proximity to Starved Rock State Park. Or check the National Historic Registry for some really "fancy" names of landmarks and go from there. I always liked simple names, like "The Market Street Pet Resort".

Good luck!! I think there is alot of demand for upscale pet boarding!