That option, at least for the “regular ones” has been in game since at least Cata. 
Unfortunately idk where the trainer is for the Horde locks though, as I stated earlier.
And apparently there are these new demons that are glyphed or something that cannot be changed(Much thanks for bringing that to light, @Arturas!!!)
Much thanks for adding this in!!
Transmog inspired system would work pretty good here. This system would add customization and be different enough to not take anything away from a hunter identity.
I would call the system the Grimoire. Each page would contain a specific minion/appearance which would be collected through creatures, quests or even a few from inscription.
https://wow.gamepedia.com/Warlock_trainers
Has a list of the name changers. The ones listed in the ‘Demon trainer’ column
Definitely good to know, though.
I leveled my lock to 120, then sat her. lol I just…idk she’s one of my “originals” so I feel obligated to level her just b/c of memories I hold with her for the time I DID play her, but outside of that I haven’t really done anything with her since MoP.
Thank you again, though!! Just sad they don’t allow that option somehow to be worked in for the ones you’re speaking about. 
Queue random DH talking to young Illidari recruits. “I’ve sacrificed everything, what have yo~”
/DH is yoinked through a portal and pops up in front of boss X"
“What have you…wait where am I?”
But real talk, why can’t Warlocks change their pets to tank or dps types. I’d love to rock with my Fel Succubis on my Warlock. But alas, shes useless outside of looking fabulous. Though truthfully, considering how bad the blueberry is at holding aggro…likely wouldn’t be much of a difference.
I’ve had a warlock for 15 years and never once used my succubus, its very sad.
would this be at the expense of being able to enslave?
Yea, pretty much. I know they have uses in PvP, or used to. Not sure if they still do. I’d imagine with all the Greater Pyro’s and Chaos Bolts and whatnot, Fel Stalker is probably more desired.
But I’m right there with you. World stuff? Void. Dungeons? Fel Stalker. Raid? Imp. Think the only time I’ve ever actually used my Succubis was after I farmed the Orb thingy from Cathedral of Eternal Night to turn her into a Fel Succubis. Then I just stood around town with her out for a bit, lol. Such a shame too, cause that model is gorgeous.
They took the abilities off of the pet and put them on the Hunter. In SL we will have to spend six seconds summoing a felhunter if we want to interrupt a spell. While you, you simply press a button and solve your problems.
The revive/summon time increase is really dumb. I get that its for PvP, but like, only change it in PvP content then.
Maybe if we keep whining they will change it to pvp only?
we’d rather you didn’t play demonology™
We can’t even name our demons and if we want a different name it costs 50 gold for each time It also costs us a soulshard to even summon an imp…and it doesn’t cost hunters anything except casting rez. There were a couple times I was toast when I lost my pet and couldn’t summon because of no shard. There was a time when it didn’t cost a shard for any pet then they changed it.
It’s frustrating as hell things are one way for an expansion and they go bipolar and completely switch it for the next.
Ok done venting, nobodies going to listen anyway.
(X) Doubt
warlocks, hunters, and druids have the most flavor / extra class fantasy in the game. Do work on literally any other class.
You know the drill.
I was going to suggest more types of undead for unholy DKs too you know. Like Dark Rangers or Valkyr instead of the skeletal archer.
Honestly I’d just he happy if my warlock could summon a nathrezim. They’re my favorite demons.
Like lust?
Succubi have lust too 
And a lot of stamina too!