I should probably clarify what I mean by DM. In a system with 3 midfielders it's pretty clear – DM is a player who sits in front of the centre-backs and plays more centrally and usually a bit further back (although they can switch places during the game) than his midfield partners on both sides. Can started the season playing left-sided CM in a 3-man midfield, but starting with the Sunderland game he took over the DM anchor role and, like I said, even when Lucas was fit Klopp chose to find another role for Lucas rather than move Can from this position.
In a system with 2 midfielders, the roles are much more evenly aligned – but still if you look closely there tends to be a certain division of responsibilities. I think in the partnership with Hendo, Can is more of an enforcer while Hendo is tasked with more attacking and playmaking responsibilities (which he's not doing too well right now) as well as constant running and high press. It's the same when Allen plays instead of Hendo – he has more of a license to drive forward, while Can has to stay alert for the times we lose the ball and he has to snuff out the counter-attack. So technically he would be called a CM in this case, but not all CMs are the same.