Hester seems the clear favourite.
Fridgedoor Hesper is a name, but it is admittedly pretty rare. It's from the same root as Vesper. Love Vesper but the Bond Girl thing puts me off.
Phunt I like Hephzibah but it's too out there even for me! I'd definitely call a cat it though 
Esther is lovely but too close to a family member's name.