Nope. Just the pokemon you'll be using, and your "signature pokemon" the one that's your favorite or you're known for.

Btw, when I said in the vein of, I didn't mean it had to fit those descriptions. I meant any theme will do, provide it's reasonable and not designed to simply build a team of 6 self destructing electrodes.

I'm going to go with the Thunderstorm theme. Electric and Water.

Sorry to rain on your parade. Whooosh!

I will adhere to a fighting type E4. I'll just make it work somehow.

My pokemon selection is greater than 6 different pokemon, but I will follow the original rules of:

4 pokemon of the primary type at least.
Up to the remaining 2 pokemon must have at least one move of the champion's type, but do not have to be the E4's type.