More or less relevant, the discussion is always open
I've ended up on conclusion to take free hands on naming the units: use a certain convention and try to keep at it.
To me "peitsimies" sounds too much like a regular melee unit, not a horse based unit that it is. Also many of the current "most common" terms used in articles and such are what they are because, I guess, nobody hasn't put real thought for better names and they've ended up with somewhat direct translations, or just using what they've seen used before. Yet the names aren't "common knowledge", I had to really dig into the internet and a few books to find these words in use.
From the English side there is a minor issue with Civilization as a series as well: some unit names are as they are due to game's own history, which means they've kept the existing words. The unit names aren't following any specific convention. An example: word "Infantry" is actually used in English language for any foot troops regardless of the era, not only for the modern time infantry. The same issue exists with "jalkaväki".
For the moment this has lead me to the conclusion of "use the main weapon name unless there is a better suited term for that type of unit". This means some units like Immortal (Kuolematon) and Companion Cavalry (Toveriratsuväki) do come quite directly as you simply can't name them via the weapons they used as there is nothing special in them. Generic units are a different story, so I've simply ended using the name of weapon with units like Rifleman (Kivääri) and Infantry (Rynnäkkökivääri).
But it is now quite a while I last had any thoughts on this matter. I still haven't gotten myself to continue with the translation, even though I have promised to have a release next month. Some annoying projects just simply don't die... I guess I won't like this restart a lot as the first thing to do is to check all the changes that have happened in the localization frontier. When I started the only good way to translate was to replace English strings, but for some reason they'd prefer other means... which were still under development at the time. Then there is the list of changed strings that I need to gather for myself.