A detailed abstract of a book (Riho Grünthal, Livvistä liiviin. Itämerensuomalaiset etnonyymit [= Finnic ethnonyms], 1997) on “names referring to Finnic groups either linguistically or geographically.” The basic breakdown:
1. Proper nouns that entered the language as proper nouns or that are merely opaque: (Finnish) eesti, liivi, lyydi, Inkeri, Suomi, vatja, vepsä, (Latvian) Igaunija.
2. Proper nouns that originally referred to a smaller area, i.e. only a part of their present-day denotation. These types of ethnonyms sometimes closely resemble place names: (Finnish) Inkeri, Karjala, Suomi, vatja, Viro.
3. Proper nouns that have lost both their connection with the original common noun and semantic motivation: (Finnish) Karjala.
4. Expressions with a transparent common noun origin: (Estonian (Votian)) maakeel, maarahvas, (Livonian) kalàmi’eD, raandali.
5. Ethnonyms that are used only by non-Finnic-speaking tribes: (Estonian) Eesti (originally), (Swedish) finne, (Russian) chud’.
There are discussions of the etymologies of Finland, Suomi, Karjala, and many other terms. For Finland:
The name Finland (Swedish) Finland, finne ‘Finn’ has never been used by the Finns themselves. The oldest record (Tacitus 98 A. D.: fenni) and the compound word structure of Finland lead one to conclude that finne must be considered a primary alternate for Finland.
The stem finne (< findo ‘Finder’ < *fenthan- ~ *fenthn-) may originate from the same word as (Old High German) fendo, (Middle High German) vende ‘pedestrian; wanderer’ (*fanthian-), (Old High German) fand_on, (Anglo-Saxon) fandian ‘research; try, check’, (Middle High German) vanden ‘visit’, (Gothic) finthan, (Old High German) finthan etc., ‘find, notice, get aware’, etc. The original meaning suggested for finne by Hultman as early as 1896 is ‘wanderer’, an explanation describing the way of life of the people (cf. (Livonian) kalàmi’eD ‘Livonians; fishermen’). This meaning conforms with what Tacitus wrote about the fenni. Fishers, hunters and people with no permanent dwelling place may be appropriately described as ‘wanderers’.