In Commander can a player deal combat damage to the same opponent's commander and accumulate commander damage across multiple turns?

Yes, combat damage dealt by a commander to a player is tracked cumulatively across the entire game, regardless of how many turns or combats it takes. This is codified in the Commander format rules (CR 903.10a): a player who has been dealt 21 or more combat damage by a single commander over the course of the game loses the game.

The damage count is persistent and does not reset when the commander changes zones (e.g., goes to the command zone, gets tucked into a library, or is recast). What matters is the permanent card identity of the commander, not any particular instance of it on the battlefield. CR 903.10a specifically tracks damage dealt by that commander regardless of zone changes.

Each player tracks the damage they have received from each opponent's commander separately. So if three opponents each control a commander, a player could theoretically be eliminated by any one of them reaching the 21-damage threshold — it is per-commander, not cumulative across all commanders.

Concrete example: On turn 5, your Atraxa, Praetors' Voice swings for 4 commander damage to an opponent. On turns 6, 7, and 8 it deals 4 more each time, totaling 16. It then dies and is recast. On turn 10 it connects for 5 more — that opponent has now taken 21 commander damage from your Atraxa and immediately loses the game, even though the damage was spread across multiple turns and a zone change occurred.

Key rules to reference: CR 903.10a (commander damage rule in the Commander format rules) and CR 903.10b (the damage is tracked even if the commander changes zones). Always note that only combat damage counts — damage from abilities or spells does not contribute to the commander damage total.