Interesting play style that we started in my group. Also the rules for it are mainly so that you can take a normal EDH deck and use with little modification.

1. Planeswalker is your commander termed "General".
2. The previous commander is now in your deck.
a. That commander is now your "Lieutenant"
b. "Lieutenant" sets your color identity
1. "General" must abide by the color identity
c. If "Lieutenant" and "General" are on field together "Lieutenant" gets +3/+3
3. No other planeswalkers can be in your deck besides the General
4. The "General" is not counted in your deck card count of 100.
a. This is to allow any deck to quickly be modified to work with this format.
5. All other rules for EDH apply.
a. "Lieutenant" has no protections for changing zones like the "General" or Commander does

As Planeswalker EDH is sorta wordy, I think General is the best name for this style.

sounds cool.

there was someone who used as PW general, and consistently fetched , and filled the deck with tonnes of mana-rocks to consistently turn 2 or 3 infinite mana kill the table. just so you know such a thing exists, and not to spoil your fun!

i think the +3/+3 sounds like a cool idea, but might make more sense if they were both in your command zone, and THEN the lieutenant can't go back to the command zone. otherwise, it'd give the players who happen to find it a huge bonus, and you wouldn't be able to check for colour-identity.

I think it sounds overly complicated with no real gain. I would suggest just trying out planeswalkers as the commanders for your decks. (I think chain veil may need banning)

I made a fun commander deck.

Yeah rings could be pretty brutal as well. Not sure on Tezz, it could be he is just too oppressive. I used him in a dack fayden build based around artifacts. Chain veil was the worst offender.

The Lieutenant part kinda concerns me because it encourages as much as if not more than the singleton nature of the format.

I think a better way of doing this would have your life counter be your planeswalker's loyalty and if your planewalker runs out of it, you lose the game. Cards that say destroy or remove planeswalkers just cause them to go into the command zone. If your planeswalker is in the command zone, any damage you take is redirected to his or her loyalty.