Alphinaud Leveilleur

Once the game begins, your two commanders are tracked separately. If you cast one, you won't have to pay an additional {2} the first time you cast the other. A player loses the game after having been dealt 21 damage from one of them, not from both of them combined. Command Beacon's effect puts one into your hand from the command zone, not both.

Note that the target player searches their library (which may be affected by effects such as that of Stranglehold) and that the card they find is revealed, even though these words aren't included in the ability's reminder text.

The triggered ability of the "partner with" keyword still triggers in a Commander game. If your other commander has somehow ended up in your library, you can find it. You can also target another player, whether or not they have that card in their library.