In Commander, if your commander is exiled face-down by Morph, can you move it to the command zone?

A card's status as your commander is a property of the physical card itself, not its face-up identity or any characteristics it currently has. Even when your commander is exiled face-down (such as by an effect like Morph's exile-face-down ability or a card like Pyxis of Pandemonium), it is still your commander. The Commander rules explicitly track the card object regardless of its visible characteristics.

According to CR 903.9, if a commander would be put into a graveyard or exile from anywhere, its owner may instead put it into the command zone. This replacement effect applies the moment the commander would move to exile — so you can redirect it to the command zone instead of it being exiled face-down in the first place. You do not have to let it go face-down and then retrieve it; you intercept the move at the point of exile.

If you did allow it to go to exile face-down (for example, you chose not to use the replacement effect), you may still move it to the command zone later. CR 903.9 also allows a commander in exile to be moved to the command zone as a special action (effectively a state-based-like option available to the owner at any time), so you are never permanently locked out.

Importantly, opponents cannot secretly use information about your face-down exiled card to identify it as a commander — but you, as the owner, always know which card is your commander, and the rules do not hide that fact from the tracking of its commander status.

Example: An opponent casts Swords to Plowshares targeting your commander — wait, wrong zone. Instead: an opponent uses an effect that exiles cards face-down. Your commander would go to exile face-down. You may immediately apply CR 903.9 and move it to the command zone instead (paying the commander tax next time you cast it). If you let it be exiled face-down, you may still move it to the command zone at any time before the game ends.