What’s the one-word translation of the word ‘cuckold’ in Greek, when the husband knows (and does not care) about his wife’s infidelity?

Huh.

As it turns out, reading Cuckold – Wikipedia, there was an Elizabethan term for someone who was aware of being cuckolded, but cuckold wasn’t it:

One often-overlooked subtlety of the word is that it implies that the husband is deceived, that he is unaware of his wife’s unfaithfulness and may not know until the arrival or growth of a child plainly not his (as with cuckoo birds).

A related word, first appearing in 1520, is wittol, which substitutes wit (in the sense of knowing) for the first part of the word, referring to a man aware of and reconciled to his wife’s infidelity.

Wittol is of course antiquated, and the kink associated with cuckolding (which is all about the partner being aware of the fact) is a pretty recent phenomenon. Wikipedia in fact makes a point of saying that this usage as a fetish is distinct from the traditional use of cuckold.

The Greek for cuckold is κερατάς ‘horned’, and has been since at least Michael Psellos in the 11th century, who documented the term. As OP notes, the Greek expression, like cuckold originally, is unaware of being cheated on; per Λεξικό της κοινής νεοελληνικής its secondary meaning is ‘a sucker, someone clueless’. (How the tertiary meaning ‘someone cunning, scoundrel’ comes about is one of those routine oddities of language.)

SLANG.gr (Hi, Melinda!) would be the obvious place to find an expression for something like this in Greek—even if they are expressions made up by site contributors. But I didn’t. The closest I got there was calling someone a Reindeer or Rudolph (τον/την έκανε τάρανδο, ρούντολφ – SLANG.gr) for being repeatedly cuckolded. As in, having really big horns.