I've put the callsigns in alphabetical order, along with the number of vessels that callsign has been applied to (or, if you like, the number of vessels that cosmonaut commanded under that callsign). I have assumed, though can't find clear confirmation yet, that if a vessel goes up with one commander, docks, swaps crews, and comes down with a different commander, that it will use both commanders' callsigns at some point. All sources I've seen only ever seem to list the launching commanders' callsigns.
I'm also uncertain about the interaction of crew callsigns and space stations (the Salyuts and Mir). As far as I can tell, crew callsigns have never been applied to the stations hosting the crew, but this is sketchy.
There are some complications with transliteration between Cyrillic and Roman alphabets, and I hope I'm giving the best possible versions. I only know enough to know that I'm probably getting something wrong. I plan to add all the Cyrillic spellings to this table at a later point, so anyone who knows better can correct me.
Obviously, there's some overlap between themes, especially between astronomy and mythology, but also between a lot of the geographical features. I've aimed to identify the intended theme as accurately as I can find, but finding isn't always easy.
The two big meta-themes seem to be "shit we can spot out the window from space" and "vaguely sciencey shit", with a smaller number of interesting exceptions.
[EDIT: Two sources I've found most useful are this discussion thread, and this list (in Russian). The latter illustrates clearly (in Russian) how the junior crew are assigned sub-callsigns per mission.]
Reminders to self: Add column for cyrillic, and wiki links for cosmonauts.
|Berkut||Pavel Popovich||2||Golden Eagle||Bird|
|Favor||Sergey Ryzhikov||1||Mount Tabor||Mountain|
|Karat||Pavel Vinogradov||2||Carat||Mass Unit|
|Kedr||Yuri Gagarin||1||Siberian Pine||Tree|
|Tian Shan||Salizhan Sharipov||1||Tian Shan||Mountain|
1. Not to be confused with the shuttle Buran. Anyone know what the plan for crew callsigns was going to be if Buran had become operational?
2. Possible mistranslation?
3. Often mistranslated as 'cedar' or 'Siberian cedar', just because it sounds a bit similar.
4. Arguably 4 vessels, if you count the unsuccessful launch of Soyuz T-10a.
5. Not to be confused with the Apollo 16 LM, nor the new MPCV.
6. I can't seem to find a good reference now, but I remember reading years ago that Roman Romanenko had wanted to re-use his father Yuri's callsign of Taimyr, but this was overruled. Even so, I still keep finding sources that apply that callsign to him, instead of Parus.
7. I struggled to find this one, and got only a single reference on some unofficial forums. Confirmation would be nice.
8. Not to be confused with the Proton rocket.
9. Possible mistranslation, as this also seems to translate to skiff (as in the boat type, which would fit well with Fregat) and scythe (as in the agricultural tool, which seems out of place on this list).
10. Soyuz is a special, unusual case, and arguably was the name of the vessel (with the mission code of Soyuz 19), regardless of which cosmonauts were assigned to it, and not the callsign of its commanding cosmonaut. However, since Leonov never commanded any other mission, this does appear to be his de facto callsign either way. The name does translate to Union, but in this case, this callsign was definitely named after the vessel class, the Soyuz, and not after the Soviet Union (which is what the class was named after, so it's not maximally simple).
11. Possible mistranslation, as Uran also means uranium.
12. Not to be confused with the Vostok spacecraft.
13. Note discussion about this one in the comments.
14. Burlaks arguably fit into several categories (e.g. rivers, navigation, water, maybe even demonyms), but not into any one especially well, so I'm assuming for now that it's better to put that name into a new category of its own.
15. Altair appears to be the first callsign transferred from one commander to another, when Padalka retired not long before he was scheduled to command Soyuz MS-06. Misurkin took over the mission, and apparently also the callsign.