Actually "coin" was not really a very good choice (as Andreas M. Antonopolous has pointed out many times) as "coins" are a very bad metaphor for how Bitcoin actually works.
The problem with new technology is that "old words" just don't fit very well - so I'm guessing the name was chosen to basically make it clear that it is a type of "money".
So if it were to be renamed the "coin" part would be what I'd drop - maybe "Bitmoney" might have been better.
if we have to rename it anyway...
Bitium or Bithium. best I can think of considering that it is mined and dividable (like precious metals).
both names are taken by some companies though. and apparently -ium is supposed to be used to denote a metallic name.
or if the "bit" part also have to be removed, Inthium or
BTCinthium... sounds weird?