Today I was googling the old name versions Belize for a text I was making, and thought I'd put the two naming theories I found on the forum, before I delete them:
One theory is that the name 'Belize' has its roots in the country's early history and comes from the name of a Scottish pirate who created the first settlement in Belize in 1638, Peter Wallace. From Wallace came the River Wallix which is also called the Rio Valis (or Balis) and later became Ballace, and finally the Belize River.
Others believe that it is a derivation of the Mayan word 'beliz,' meaning muddy waters.
This way I know where to easily find them the next time.