Anon means soon, or in a little while, in old use. See you anon, more of that anon, anon he came.
It is archaic and now used almost entirely for effect — more of that anon is the one phrase still in circulation, and it is knowingly old-fashioned. The abbreviation anon. for anonymous is a different word entirely. Note that the original meaning is in one moment, from the Old English for in one.
1adverbanonSoon, or in a little while.
“Enough about the wedding for now; I'll tell you more anon.”
anon is a measure of time.
Middle English anoon means in one moment, from Old English on plus an, one. The abbreviation for anonymous is unrelated.
Middle English
anoon
English, today
anon
From Middle English anoon, anon, anan literally “in one (moment)”, from on + ān. See on and one.
Etymology from Wiktionary, CC BY-SA