It wouldn’t have been known if he always had hidden it behind an eyepatch. People need not even suspect that there was anything other than a missing eye.
When Alastor Moody had lost his eye, he had commandeered the services of a most erudite Ravenclaw, Samuel H. Lyall, whom Moody mistrusted slightly less than average because Moody had refrained from reporting him as an unregistered werewolf; and he had paid Lyall to compile a list of every known magical eye, and every known hint to their location.
When Moody had gotten the list back, he hadn’t bothered reading most of it; because at the top of the list was the Eye of Vance, dating back to an era before Hogwarts, and currently in the possession of a powerful Dark Wizard ruling over some tiny forgotten hellhole that wasn’t in Britain or anywhere else he’d have to worry about silly rules.
That was how Alastor Moody had lost his left foot and acquired the Eye of Vance, and how the oppressed souls of Urulat had been liberated for a period of around two weeks before another Dark Wizard moved in on the power vacuum.
He’d considered going after the Left Foot of Vance next, but had decided against it after he realized that would be just what they were expecting.
Apparently he was unable to obtain the Eye of Vance secretly. Besides, the presence of Moody plus the death of a dark wizard known to possess the Eye of Vance plus the missing Eye of Vance is enough to conclude Moody has the Eye.
It wouldn’t have been known if he always had hidden it behind an eyepatch. People need not even suspect that there was anything other than a missing eye.
Apparently he was unable to obtain the Eye of Vance secretly. Besides, the presence of Moody plus the death of a dark wizard known to possess the Eye of Vance plus the missing Eye of Vance is enough to conclude Moody has the Eye.
There’s still a big difference between a very few very knowledgeable wizards hearing about it, and flaunting it everywhere he goes.
I’ve already outlined how a merely knowledgeable wizard can conclude with some degree of certainty that Moody became the owner of the Eye of Vance.
It only required specialist Ravenclaw research to obtain an extensive list of magical eyes. We don’t know how famous the Eye itself is.
What about signalling / intimidation?