We all know that "a lot of RPers" includes you, Dave. It's all right, you can admit it.
More on-topic, though... one easy way to find different names would be to take a descriptive term and translate it into the native language of the state in question. For instance, my original secondary nation, Ubakasa, took its name from the Hausa words for father (uba) and land (ƙasa), though admittedly that's not evidently the Hausa term for fatherland (that instead is kasar uba). Neither Kalmyk, Buryat, or Tuvan are available in Google Translate (my typical go-to for this stuff), but if you wanted, say, Ukrainian names, you could have the following (with literal English translations):
Batʹkivshchyna ("homeland")
Peredhir'ya ("foothills")
Bilyudy (derived, probably incorrectly, from "bili lyudy", meaning "white people")
If you want authentic-sounding names, my recommendation is to pick a language you want associated with the country in question and play around with different translations in your preferred translation software until you find something you like. Then, of course, record the derived meaning somewhere so you can use it as trivia in the future.