Count Dooku killed Jedi Master Sifo-Dyas and impersonated him in order to order the Clone Army. Since Dooku ordered the Clone army, does that mean the Clones know Dooku is the one who ordered them; if so, do the Clones know that Dooku is Tyranus?
I do not believe there is a Cannon answer.
There is no evidence to suggest they even know the existence of Dooku, Tyranus or Sifo-Dyas
I believe that Dooku placed the order for the Grand Army of the Republic and never made contact with the Kaminoans. This is supported by the fact that the Kaminoans expressed that they were concerned by the lack of contact from the Jedi/Republic since the order had been placed. Kenobi's contact with them during Attack of the Clones seems to be the first contact since the order was placed.
The only source of ambiguity is what Jango Fett knew/revealed. Jango knew of the existence of Tyranus as he was recruited by him:
"I was recruited by a man called Tyranus on one of the moons of Bogden."
Jango during training sessions, Jango may have mention/revealed that Dooku was in fact Tyranus.
It was unclear whether Jango knew of Sifo-Dyas or that Tyranus ordered the clone army under the pseudonym. Jango claims to not know the name; however, that could be a ruse to throw Kenobi off. Perhaps the Kaminoans mentioned that the army was ordered by Sifo-Dyas; however, the Kaminoans seem to strictly follow a need-to-know basis when it comes to information. I do not believe Jango knew about Sifo-Dyas.
The amount of contact that Jango had with Dooku/Tyranus is unclear. It is possible/likely that Jango could have put two and two together. Dooku is a well known political figure, Jango knows Tyranus and is a smart man who is well connected. I believe the Jango knew or strongly suspected that Dooku was, in fact, Tyranus.
If clones did know Dooku was Tyranus, it would only be the original clones and, probably, only those who received personal training from Jango Fett himself. Even then, I find it highly unlikely that Jango would engage in small talk about Dooku and Tyranus with the clone troopers.