Does damage dealt to a player by a commander count toward commander damage if they were given control of it temporarily?

Commander damage is tracked based on which commander deals the damage and which player receives it — not who controls the commander at the time. According to the Commander format rules (derived from CR 903 and the official Commander rules), 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.

Critically, the 21-damage threshold tracks damage from a specific commander (identified by its card identity) to a specific player. If an opponent temporarily steals your commander using a card like Bribery, Zealous Conscripts, or Control Magic, any combat damage that commander deals to you still counts toward commander damage — because it is still YOUR commander dealing damage to YOU as its owner's opponent. The tracking does not care who is currently controlling it.

Conversely, if you are given temporary control of your own commander (an unusual scenario via certain effects), damage it deals would still be tracked by its original commander identity against each player it hits.

Concrete example: Your Ur-Dragon commander has already dealt 15 combat damage to you this game. An opponent casts Insurrection, takes control of The Ur-Dragon, and attacks you with it dealing 9 more combat damage. That 9 damage counts as commander damage from The Ur-Dragon — bringing your total to 24 — and you lose the game.

This is because the Commander rules track damage per commander card identity per player damaged, regardless of who controls it (Commander Rules, supported by CR 903.10a analogue in the format's supplemental rules).