if digit is the name for a number on base 10, what would be the name for a number on base 16? Hexgit?
Digit. Simply a hexadecimal one.
Are you looking for an analogue to bit for binary digit? Hexgit wouldn't be my choice; it doesn't really roll off the tongue. As for the unit of storage, a hex digit represents a nibble's worth (or nybble).
The word 'digit' can be used in any number system. The only exceptions are 'bit' which is really just short for 'binary digit' and 'trit' which is short for 'ternary digit'. (You can still call bits and trits 'digits', however.)
There isn't really a consensus, I don't think, but see http://en.wikipedia.org/wiki/Units_of_information for some options.
Personally, I'd just say "hex digit".
One of the elements that collectively form a system of numeration.
"Hexgit" would be a bad choice since "hex" formally suggests base six rather than 16.
"Hexdecit" would retain the 6+10 representation, but I would stick with "digit".
"Hexdigit" and "hex digit" are both in wide use in textbooks.