Try entering "/invisibility_mode 'yourName' false" in the game's chat, it might've been turned on by default due to a bug. If that fails, you might have to make a new universe. Make sure that your ships are saved as blueprints before doing so, so that you can respawn them in the new universe.
If that does not work, try to do a fresh installation of your game. VERY IMPORTANT: Save all your ships/stations as blueprints. Then back up your blueprint and server-database folders (in your starmade folder), along with the keyboard, and settings files (copy/paste them somewhere else on your computer). Delete the entire starmade folder and re-install with the use of the launcher. You can then re-add the files you backup up earlier back into the game's main folder.