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There are some organised Orc Military units in Orsinium and at Shinji's Scarp in Stormhaven. They use the generic English military ranks - Sergeant, Lieutenant, Captain, General (in the English version of the game).
It might be more fun to invent your own ranks for your own unit, e.g. half-tusker, tusker, grudge master, spite warden, little goat (for LT's of course).
@Enodoc and @RaddlemanNumber7 are right, OP. I'll just write a bit more to support their words. The semi-nomadic Orcish tribes are a society very similar in it's type to the Dunmeri Ashlanders' one, though with only one exception - they are at their final stage of the primitive, tribal, type of society and are very close to feudalism. The communal relations between relatives are still very strong but the social inequality and the division of labor begin to differentiate common tribesmen from their chieftains and kings. The Orcish type of society and their city of Orsinium are similar to the society type of the semi-nomadic Turkish Oghuz tribes especially its Seljuq branch of the XIII century and the Sultanate of Rum IRL respectively. The Orcish relations with the Breton feudal kingdoms and the Empire are also very similar to the Seljuq Turks relations with the Crusader Kingdoms and the Eastern Roman Empire IRL.
Ranks or military titles, if you meant those ones, are common to regular armies and, as you have mentioned it, the Orcs do not have one yet, thus there are no purely Orcish ranks except that "Chief" title. Even the chief's assistants are called simply.. assistants like that Chief Gloorot before he became the chief. But yes, @Enodoc and @RaddlemanNumber7 are right - some distinct military units use those ones common to us. In order to create a regular military organization the Orcish society has to:
1. Develop it's social division of labor further on;
2. Create the two main classes of feudals and peasants where the military estate would be a feudal class's estate.
3. Unite the clans under the rule of feudals with a high king;
4. Conquer territory to establish an Orcish state.
All these four terms are equal in their value and must be achieved in order to build an army you speak of. The constant building and destruction of Orsinium is one of the things that prevents it.
Guilds are the product of late feudalism: legalized in 2E 321 by the Guild Act they are the first capitalist companies established in the Second Empire for financial gain instead of subsistence production, they are too far ahead of the Orcish society. If you wish to create an Orcish guild, you could use something other than ranks, something corresponding to the very beginning of the Orcish social devision of labor: a chief as a head of the guild with his assistants, hunters, gatherers, merchants, warriors and smiths as other equal or almost equal "ranks". You could also make some "wives ranks" such as "forge-wife", "hunt-wife" and etc., but I doubt too many girls play the Orc characters. Or you could also use those traditional Alliance military ranks @RaddlemanNumber7 told you about, if your guild is something like a private military company abroad fighting for an Alliance. But there are there 26 ranks.. Anyway, those ranks depend on the type of guild you have created. If you could provide us more information on your guild, we could offer you some other more precise ideas.
You could perhaps use the '-wife' titles as a basis, so we see things like Forge-Wife and Hunt-Wife, perhaps your guild could use Forge-Master, Hunt-Master etc.
Or perhaps you could visit some Orcish areas with enemy NPCs since they'll have culturally themeatic titles to differentiate their roles from a gameplay perspective. For example, the Lhurgash Wood Orcs in Greenshade have generic NPCs called Bruisers, Ravagers, Rangers, Warriors etc.
Its unlikely that Orcs utilize anything beyond a basic command structure as there is no need for a standing army of the type we would find in a medieval fantasy setting to have anything overly complicated like you see in modern military's.
I'd suggest replaying the Orsinium quest at Frostbreak Fortress, where we see King Kurog lead his army to deal with the Winterborn Reachmen.
For example, one of the NPCs we help is "Siege Commander Dulph".
Siege Commander is a title not a rank. Its meant to convey the duties he has been charged with rather than the position he holds in Kurogs army. He may very well be a commander in Kurogs army if that is a rank they use. In all actuality anyone charged with overseeing the siege would hold this title so someone as low as a sergeant could potentially act as the Siege Commander if he is the highest ranking person present for the siege.
This way there is a clear command structure to the activity and there isnt confusion in orders and commands being given during the course of the siege. Without Dulph fullfilling the clear cut duty of siege commander another general could show up on the scene and start barking orders which would create even more chaos than a battle already brings. With Dulph filling the siege commander role there is a specific person the men understand they need to listen to and all instructions come from and go through. That newly arrived general would need to either address Dulph or Kurog to implement any changes he would like to see because of that title. Dulph could even ignore higher ranking members of the Army if their orders and commands go counter to instructions he has received.
I can only speculate but given how Orcish society tends to be rather patriarchal my guess is that ranks would be as follows:
Warchief (a chief chosen by the other chieftains to lead them in war)
My guess is that they wouldn't make up some fancy new military ranks but just stick to the ranks they already had before. The chieftain is the most important rank who everyone needs to listen to. In the rare case several clans can agree on something, they choose one of their chieftains to be the warchief. All their wives are now integrated into the chain of command as well and every capable Orc left is automatically a warrior.
Now I do see why this wouldn't work too well to adopt for your guild, but I'd say it's probably the most accurate of how this would actually go. MarshRangerHaz's proposal to swap "-wife" for "-Master" is a good call though for the sake of running your guild.
This Bosmer was tortured to death. There is nothing left to be done.