Mungojerry and Rumpleteaser are boys, silly! 
She doesn’t sound much like a Griddlebone, so Jennyanydots is pretty much it for female names from T.S. Eliot. I’d never noticed the gender imbalance in the poems before.
Jenny is a great name for a cat. Of course, you’re familiar with the Paul Gallico novel of the same name…
We want pics!! We want pics!! From your description, though, she SOUNDS like a Jenny. Smooches to her from me and chembug, 'K? Smooches all around!!
Propose naming scheme for cats: Pestilence, Famine, War, and Scooterpie.
Have 15. I think. Somewhat hard to count.