Demon Hunter - what's in a name?

The Demon Hunter class is not a class that hunts demons. It is a class that uses demons to hunt. 

Does this mean there might be a Demon Mage, or Elemental Mage?

Feels like Demon Warlock might fit better?

Or am I just overthinking it, and they just wanted something that sounded acted really SMOrc-y?

"Face Hunter was popular, lets use DEMONS and make it a whole class."

In WoW lore, Demon Hunters are exactly that, hunters of demons. They do have Demon allies, yes, but they ally with them strictly in order to bolster their army and be able to hunt even more demons. 

Quote From Author

It's is a class that uses demons to hunt

...demons ;). That pretty much sums up their lore.

This is a WOW class and not something the HS team made up

https://worldofwarcraft.com/en-us/game/classes

We are only missing death knight and monk.. if demon hunter is a success I think we will eventually get the other 2.

I don't think they will make death knights in HS, since there are already some death knights as heroes. I say it wouldn't make sense. But monk will for sure have a class if dmh goes well

I think for gameplay reasons this is not the case for dhunter in hearthstone.

Quote From Techwood

I don't think they will make death knights in HS, since there are already some death knights as heroes. I say it wouldn't make sense. But monk will for sure have a class if dmh goes well

It's quite possible.. they just need to reword 2 card (the Lich King and Arfus) and the design space is there.

Classes having deathknight heros doesn't make the class have no reason to exist..

I think that if they add another class... (in 2-3 years from now) it would be monk first and then.. maybe in 5 years death knight so basically there's not much reason to discuss it right now and I don't think then Blizzard will take into account a decision they made in 2017...

New classes means more artwork and balance changes consideration are needed. Although, I still believe in the hope of more new classes, if the developer team wants it for developing a full dream of WoW come true. 

Quote From Techwood

I don't think they will make death knights in HS, since there are already some death knights as heroes. I say it wouldn't make sense. But monk will for sure have a class if dmh goes well

It's pointless that during an expansion they printed what are "flavored" as Death Knight: that were "Hero Card" and several others have been printed outside of said expansion set. The only thing that actually is named as "Death Knight" are the cards generated by Arfus and The Lich King, but if they ever going to introduce Death Knight as a new class they just need to rename those two.

I saw an interview with Dean Ayala somewhere and he is completely open to the idea and possibility of adding new classes if  the feedback is positive with Demon Hunter.

And as the others have pointed out, Demon Hunter is a class in WoW.