Oh wow, how adorable!!! As far as giving the new arrival a name, I always wait at least a few days so I can see what kind of personality shines through.
I have two cats that were rescues and both of them picked their own names just by their quirky personalities. I recently wrote a short article about how they came by their names if you'd like to see what I'm talking about -
Pet stories: How my cats got their names - by Erin Ahmed - Helium
You never know though, something might just pop into your mind and you go - that's it!
Erin