The Hamlet Project

Probably, before cameras, royals could conceivably walk around in relative anonymity if they wanted to. Just take off your crown and you have an instant cloak of relative invisibility. I mean, we see Henry the V do it in that play. Here Hamlet can play dumb about basic Denmark facts and presumably the grave-maker is none the wiser.
How would he recognize a prince? By his portrait? Probably not in person. There not being much call for the overlapping of gravemakers and princes usually.
There are no photos, no videos – just paintings and drawings and engravings, which, no matter how artful, don’t necessarily make their way to the eyes of the people.
I think if I were a royal, I’d take great solace in being able to throw off my royalty for a moment and just wander as a human. I’d probably also have to be a male royal to make that really work, though – as ladies didn’t have quite the freedom of movement that I’d find optimal. Maybe, if I had been a queen, I’d have periodically dressed as a man to go out exploring.