There's an interesting reason for that.
Although English contains elements from numerous languages, it's two primary ancestors are French and the Germanic Anglo-Saxon.
In the middle ages, most of the English peasantry spoke Anglo-Saxon. The nobility, however, all spoke French for several hundred years after William the Conquerer invaded in 1066.
To this day, that ancient split in languages is still obvious. Everyday words in English, including words for animals, household words and swear words, tend to be Germanic: short, guttural and abrupt.
Words to do with civic society, culture and the ruling class are usually from French. They are usually longer and sound more refined. Examples: parliament, judiciary, government, etc.
Earthy words are short in French too. "Merde" is as abrupt as "shit." And German is full of long words.
What's really going on is that earthy words tend to be short, whatever their origins. And since English is not so much a mixture of Anglo-Saxon and French as a core of Anglo-Saxon with a veneer of French on top, the earthier, more basic words in English tend to have Anglo-Saxon origins.
English is what happens when Norman soldiers pick up Saxon girls.
I'm not sure why you would get a computer involved though. Why not just take a few minutes and think up words with your team, and then play with them until you have something you like? You can't possibly evaluate unlimited possibilities, so why not scope the games to words, phrases, and ideas that connect in your brain?
One thing I learned was that most short words are negative or at least excessively blunt. Webpig, Webzit, Webfat, Webdog, etc. But one name the program generated was Webvia. That wasn't so great but if you switched the words it became a reference to the fact that our software worked over the web.