When I buy a cheese from a type I don't know, I usually discard the rind, just because I'm not sure it is edible. Is there a way to tell if it is edible, other than researching the cheese type?
Bloomy: Appears white, soft, maybe fuzzy. Can also be reddish/brownish. Comes on softer cheeses that have a more custard-like flavor. Formed by a spray of penicillium candidum before aging. Edible, but the flavor changes and may taste ammoniated over time (consume so long as it's palatable)
Washed: Color ranges from pinkish red to orange or brown. Caused by bathing the cheese in some kind of solution, be it a salty brine, beer, brandy, wine or some other alcohol. Contributes to the flavor in some cheeses, and tastes unpleasant in others.
Natural: Formed by letting the cheese age on its own, drying out and growing whatever molds might be present in the cheese or air. Tends to have a concentrated flavor of the cheese, but may not be palatable. Examples: Stilton, Montgomery Cheddar, Parmigiano-Reggiano. Sometimes comes under a cloth cover. Should be edible, minus the cloth.
Additionally, there are two other possibilities
No Rind: There should be no guessing here. You've probably had cheeses with no rind...because they might come in a container. Ricotta, fresh mozzarella, and creme fraiche come to mind.
Wax/Twig/Cloth: Inedible. Should be discarded
My personal takeaway from this quick research is that I should learn to distinguish artificial covers (cloth/wax) from rinds. It seems like those that separate from the cheese will either be an artificial cover or an old rind, both of which are undesirable.
If it's indeed a rind, then I'd taste it, both alone and with the cheese, to determine if it's palatable. For Parmigiano-Reggiano specifically, I've read that it goes well in soup. Perhaps this is because it's unpalatable-y hard, but still contains the concentrated flavor.
TLDR: look for cloth/wax. If none, is it tasty? Does it feel good in the mouth?