In Commander, does a player who controls two commanders take 21 commander damage from each separately or combined?

In Commander, the "21 commander damage" rule (also called the commander damage loss condition) is tracked per commander, per player. A player loses the game if they have been dealt 21 or more combat damage by a single commander over the course of the game. This is stated in the Commander format rules (a supplement to the Comprehensive Rules), and CR 903.10 covers the commander damage rule.

When a player controls two commanders — which is permitted for certain legendary pairs, most notably via the Partner mechanic (CR 702.124) or similar abilities — each commander maintains its own separate running total of combat damage dealt to each opponent. The totals are NOT combined. So Commander A might have dealt 15 damage and Commander B might have dealt 14 damage to the same opponent, and that opponent has NOT lost the game from commander damage (though they are close with either one).

To trigger the loss condition, a single commander must reach 21 or more combat damage dealt to that specific player. There is no rule that adds the two commanders' damage totals together for this purpose.

Concrete example: You control Commander A (a 10/10) and Commander B (a 5/5) with Partner. Over several turns, Commander A has dealt 20 combat damage to your opponent, and Commander B has dealt 10. Your opponent has NOT lost from commander damage — Commander A is one point away from lethal (21), and Commander B's 10 damage is tracked entirely separately. Only if Commander A deals 1 more combat damage to that opponent will they lose.

Note: A player can still lose from regular damage (life total reaching 0), poison counters (10), or other loss conditions independently of commander damage tracking.