I like Responsible Companions too, but I can see the point of the name giving more of an idea of what the business is.

I got some Google lists of resume services for humans to see if they'd give me any ideas, but so far nothing has turned on a light bulb over my head.

I like PetCV in your poll. How about something like My Pet's CV (or Resume) or PetTenantCV? ..I don't like my examples that much, but I'm thinking there might be something along that line.

I like the Prefurred.. Refurred.. Furrever.. ones too. But then, I suppose you'd do them for roommates with feathers or fins or scales too?

Best wishes with it!