It's not going to be an overly inspirative topic, but this "issue" has really been bugging me for some time, so I need to either find a solution - or convince myself that there's nothing wrong in the first place. So, I've been working on a turn-based strategy game in which players control armies that are made out of units (doh) in a typical, cliche fantasy setting. A unit is an actual military unit made out of a number of same creatures. Think Total War or Heroes of M&M units. Consider two of the races - Human and Dwarf. Now, say that both of these races have a "spearmen" unit. The actual issues appear in naming those units (note that english isn't my first language, so I might be overlooking some things). "Human spearmen" sounds dodgy in the first place. There's a clear temptation to just call them "Spearmen", without the racial prefix. Many games have taken this approach when naming human units. I don't like that, especially with other races having spearmen units as well, but I like the sound of "human spearmen" even less. When it comes to Dwarves, I've always found it odd to use a "-men" suffix (spearmen, swordsmen, bowmen) for non-human creatures. Other games either choose to have only one unit of a specific race and just call it "Dwarves", or use more exotic unit names for non-human creatures. I've also seen both "elven" and "elvish" ("dwarven" and "dwarvish" as well) around. I've been wondering for a while if either of those is generally correct or accepted form. Any opinions on which direction is right, as well as alternative suggestions, are of course welcome. :)

Elven, elvish and dwarven, dwarvish are both fine. There seems to be an argument amongst fantasy writers as to whether the plural of dwarf is "dwarfs" or "dwarves", but I don't think most people mind either way.

I think most games either use the fantasy species as an adjective (elven archer) or occasionally replace the -man suffix with the alternative (speardwarf).

Alternatively you could use a different culture for the other species. Viking or Germanic is often used for dwarves, using units like a Valkyrie or Berserker. An interesting alternative you could use is to use your multiple languages to your advantages - you could make one side have Italian names, which would make your game a little bit different from the standard.

If the descriptions, pictures, stats, behaviour etc. make it clear enough that the units belong to a certain race and are functionally "spearmen", the actual unit name need not include "men" or "spears".
You can have generic Human/Dwarf/Elf Spearthrowers/Light Infantry/Javelineers/Skirmishers, or fancy names that don't need to be qualified with a race: King's Hunters/Hill Scorpions/Rural Militia (human), Iron Nailers/Order of the Pick/Spike Teams (dwarf).
In most games unit race is irrelevant and completely obvious from graphics: it can be mentioned if appropriate (e.g. referring to factions in the battle: "Side 2 - Dwarf Kingdom of Foo"), but there is little need to repeat it in unit names.

I prefer the idea of name them something unique. Instead of "Human Spearman" and "Dwarf Spearman".

Think about it this was. 'Spearman' is a human term and so should only be used by humans. Name the dwarven version something from the dwarves culture. And as Trapper Zoid suggested, you could use a different language for each species.

Yeah, you could replace the human suffix with like dwarf, but as Trapper Zoid said you could use other languages to give the units' names. You could use the method plenty of fantasy authors do and look at the etymology of words and create a descriptive word based on the etymology, like use Spear's etymology (spere in Old English) and make something like Spereborne Dwarf (not a great example but just an idea).

The game Slaves to Armok II: Dwarf Fortress uses the idea of replacing Spearman with Speardwarf for lots of things including Craftsman changed into Craftsdwarf. However, that can sometimes seem a little silly but Dwarf Fortress worked on some of that mild silliness.