Interleaf, which I assume that Overleaf is a pun on?
Took us about three months to pick Overleaf, we went for it largely because it was a single word, hard to confuse/mispell when said aloud (unlike writeLaTeX), had a connection with writing "over the page", and probably must importantly, we could get the .com domain.
Can you explain this part? The sound of "Leaf" could be represented by any number of possible spellings, eg "leave", "lief", "leeve"... - not all are standard English words, but neither is "Overleaf", and exotic/made-up spelling would be just par for the course for a tech product with an exotic/made-up name.
I actually really liked the domain name writelatex.com, because it pretty much tells you what you can do and it's easy to remember, even if you haven't used it in a long time (which could easily happen for a product that gets used a lot in academia and much less outside, eg someone returning to school after a few years of work).
That's an interesting point about the pronunciation - overleaf is a standard English word, and certainly seemed less confusing than writeLaTeX when said aloud, but I agree it's not perfect! Was the best we could find at the time (especially given the other needs mentioned above).