Unfortunately your options are limited here, because Blizzard decided to make those settings non-accessible.
This issue is not caused by ElvUI or any other addon. Blizzard changed the way texts are rendered and messed up those fonts, because they never planned to have them scaled up that far (remember when they talked about limiting the camera distance). Also according to some reading it is not possible for any addon to access the size, outline, etc. of the these system names.
What I've figured to be helpful so far:
Change your Anti-Alias settings. Better settings make them better to read. This will likely cost you some FPS, though. Turning AA off helps as well, but that makes the game look like it's from 1990.
Turn on nameplates and enjoy your self-designed layout using your ElvUI options.
Use ElvUI or any other addon that does that and change the font of the names. Using an easy-to-read font can be helpful as well. ElvUI can not change the size of it without nameplates enabled.
Under General click on Media
Change the Name Font to something easy-to-read
Restart the game. Reloading does nothing, because you can change it only once per session and ElvUI already did that. (You can use the Default Font option to look for your desired font in the first place and then try it out when you found one. This saves a lot of restarts.
If you run out of fonts use an addon like SharedMediaAdditionalFonts to install a bunch of additional fonts.