Does Doomcaller think my C'Thun is dead if I have multiple and only one is dead?

Doomcaller is a card in the new Whispers of the Old Gods expansion, that reads "Give your C'Thun +2/+2 (wherever it is). If it's dead, shuffle it into your deck.".

This is a scenario that I will probably encounter soon: I play my C'Thun. It dies. My opponent plays C'Thun as well. I cast Entomb on it, which shuffles his C'Thun into my deck. Now I have a dead C'Thun, and another one in my deck.

If I play Doomcaller now, will it shuffle the dead one into my deck?

(similar situations occur with other cards, e.g. cards that make copies of C'Thun before it dies)

Yes, it will work.

Doomcaller just checks if C'Thun is dead, without caring about the presence of any other copy in your deck or hand.

A reddit user had a similar experience to the one you explained in your question: he got a C'Thun from A light in the darkness, played it and it subsequently died. After played a Doomcaller he got a second copy of C'Thun added to his deck.