"Fighting Dreamers" was a Working Title while the series was in development, a literal interpretation of that one Naruto OP (since the cats were technically fighting in dreams) that later became a Permanent Placeholder
The whole Multiverse idea came from Manny/Sarah's multiple attempts to throw Sandy/Patches/Stewie into a coherent series and having it go through multiple iterations before something finally stuck.
About the Characters
A good portion of the cats are based on actual house cats that Manny/Sarah knew about in the early 2000s, mostly from friends and family
Sandy (along with Pickett, and Gracie) are directly based on the cats she's owned.
Morgan (Sandy's real life and in series sibling) flipped genders so many times in multiple iterations of Sandy/Patches/Stewie's stories that this version of them is Genderfluid and identifies as Male, Female, or neither at any given point
Pickett's in series sister (Mildred) is loosely based on a gray kitten littermate that had already been claimed before Pickett was taken home.
The original Patches was more of a cap and saddle tuxedo, like this◊, but a misinterpretation of her markings lead to the more patchy look she has now
Stewie and Fiona are loosely based on an aunt's cats. Stewie in particular shifted significantly from a cat that looked like this◊ (in real life)to something closer to a fluffy orange tabby
He's the most significant change out of the main 3 and the cats they're based on