Debian was first announced on 16 August 1993, by Ian Murdock. He formed the name Debian as a combination of the first name of his girlfriend (later wife, now ex-wife) Debra and his own first name. A nice way to name something. Take note all new Linux ditro makers.
And they also mention Mepis:
Originally, the word MEPIS didnt mean anything in particular; it came about by mistake. When Woodford misunderstood a friend over a bad Skype connection, he decided to use the name because it was a simple five-letter word and there were no other companies or products with that name.