Rabbi of Berlin
Look in Tosfos in Zevachim. 27b
btw. I once heard a pshat the Biblical Hebrew is the most encompassing language. It is just that the only parts of it we are privy to are those words in the Tanach.
It could also be the same thing with names. There were obviously more names used than just those which appear in the Tanach. It could be that there was a Mesorah that Mimon was a name. It is just that we know of this due to the Rambam. Could be the same thing with the name Chaim. It could be that it was around for a long time. Just that the first records of it was the above listed tosfos.