The Princess...
She has been a cat in search of a name. After bouncing around the "M"s for a while--Matilda, Magdalene, Madeleine--I started to call her "Mona," based on her mournful mew. Mo-mo for short.
"Princess Mona," if you want to believe her.
In truth, though, since she has fixated on Dennis as her person, his wishes have the most weight. He just refers to her as "my Precious" in a Gollum-like voice. So "Precious" is how she will be known.