Looks like in order to get all the dungeon names, some amount of trial and error is needed. Fortunately, trial and error can be assisted.
Here's a debug version of Sky Editor. In Resources\Plugins\SkyEditor\English, there's a file called RBLocations.txt. Adding lines to this file will update Sky Editor's locations for Red/Blue Rescue Team. Finding out the IDs for each location is the tedious part. Fortunately, Sky Editor can help by generating a save file with Pokémon met at every location.
How to do this:
1. Open Sky Editor and load a Red/Blue Rescue Team Save (North America or Europe). The save should have 255 free Pokémon (as shown by the ----). If not, not all locations will be accounted for.
2. Debug -> Run Command...
3. Type "rbloctest", without the quotes.
4. Save the file somewhere you'll remember it.
5. Close and reopen Sky Editor.
6. Load the file you just saved.
7. Either run the save with DeSmuMe (included, just press F5 or use the menu), or run it with your choice of Emulator/Flashcart/Legit Cart
8. Go visit a team member.
9. In the list of Pokémon, you'll see lots of "Met At X" Pokémon. Look at the summary of each one not included in RBLocations.txt.
I've attached two save files for convenience. One for each region. Unfortunately, the EU version didn't have enough free Pokémon, so not every location can be found with it. (And the North American one was made with a slightly older method, so ignore everything after Met At 255.)
If you want to do this, it would be much appreciated. If not, I can, but it might take longer.
RBLocTestEU.sav
RBLocTest.sav