Yes. The thing is both are nouns, but “property” is still acting as an adjective, it’s telling us what kind of rights. Other examples are “vacation home” and “baseball hat.” But when it’s done improperly it’s called noun pileup (see my notes on it here) like: “bank rate rise leak probe.”
Whenever only “Hank” or “Rearden” is used in AS it’s actually a shorthand for “Hank Rearden”, they’re always referring to the specific person which is Hank Rearden. Compare it with “big house.” “Big” and “house” are different concepts. “Big” can apply to many things. “House” can have many modifiers. “Hank” and “Rearden” are really the same thing. You could say “Rearden” modifies “Hank” so it tells you which “Hank” we are talking about, or the other way around. But that isn’t helpful. The words are so closely related I don’t think it’s worthwhile to give them separate nodes.