This question raises a bunch of questions I actually find more interesting, but which are, alack, out of scope of this Stack Exchange instance:
- How did the learnèd coiners of χρήστης, the Modern Greek word, get the voice of the Ancient verb χράομαι wrong? (Active: "to furnish", in particular "to furnish an oracle"; hence, as @brianpck notes, "oracle-giver" or "creditor"; Middle "to be furnished = to use")
- Given that χράομαι had fallen out of use, how did the same learnèd coiners come up with something as monstrously awkward as χρησιμοποιέω "to make useful" for "to use"?
- What on earth did the vernacular use before χρησιμοποιέω was coined? (Δουλεύομαι, Somavera's 1700 dictionary says, the middle voice of Modern δουλεύω "to work". Well, that middle voice certainly hasn't survived into the present day.)
But if we want a word for someone who χρᾶται "uses" a computer, I don't see why the middle present participle χρώμενος won't serve.
Interesting that "user" is not to be found in Woodhouse's 1910 English–Ancient Greek dictionary. It also does not occur as a gloss in LSJ. While OED reports user first used in English in 1425, it's become far more common in English latterly, with reference to computers or drugs.
Of course, Ancient Greek being Ancient Greek, χρώμενος is disconcertingly ambiguous, and LSJ reports it already used to mean "someone who consults an oracle"; "someone who takes part"; and in Xenophon, "someone who treats someone as (a friend)"—hence, "friend".
Of course, that's the strict technical notion of "user" as "someone who uses a computer". As used on this site, "user" is pretty much "site member", as a specialisation of that sense; Modern Greek would propose μέλος "member", but LSJ has that word still stuck in the sense "limb". I'd say μέτοχος "one who partakes of; partner"; the sense "member of a board" is Koine (and non-literary), but it has the right emphasis on community.