Could there be a Gnarly Man in current times?

So I’m making my way through The Best of L Sprague de Camp, and I just (re)read “The Gnarly Man”. It made me wonder ... well, first a quick summary for context:
This story was written in 1939 and is set in 1956. It’s about an immortal Neanderthal - basically he stopped aging around the age of 33. He most definitely looks the part, and he’s intelligent, articulate, knowledgable, knows dozens of languages, etc etc etc, A fundamental part of his long-term survival has been to avoid attention - nothing high profile or noteworthy, move on to a new place every 10-15 years (sooner if necessary), etc.[1]
That said, throughout his 52,000 years, he has pretty consistently been part of society, not some sort of loner hiding out in the wilds. Here, we initially find him performing as an ape-man in a carnival show. During the story he mentions he has also been a blacksmith, a maker of false teeth (he says he invented them [2]), a wagon driver (transporting goods), a professional wrestler, an archer in a Briton army (vs the Romans), a cabbie, and he ran a sawmill. (I may have missed some.)
And this made me wonder:
Given his obvious physical differences, and with modern technology and communication being what it is, are there ways he could he stay a member of modern society and also avoid attention?
Tony, having some initial thoughts, but curious about yours
[1] Poul Anderson revisits this mode of survival for immortals in The Boat of A Million Years. Of course, in Poul’s book, the immortals are modern-type humans who don’t look any different.
[2] He also invented soup, by necessity, since his teeth wore out and he hadn’t invented false teeth yet.