They can't possibly use systems with fewer than twenty characters because then the name generation would be limited. You'd be telling your friend about how you killed some Unikunians on a planet in the Hovtay system, and he'd be like "WTF!? I Killed ROMULANS on an ASTEROID BASE in the Hovtay system!"
Your immersion would be shattered. You'd delete your character, cancel your subscription, reformat your hard drive, destroy all trek-related media in your home, lose all interest in real-world astronomy and space travel, and generally give up on life.