But they're not three entirely different concepts. Regular-capital-X, the random variable, is the object. Italic-X is its range, and lowercase-x is often something like an iterator over that range.

It might be a little clunky in isolation, but it lets you talk about multiple random variables and their properties in a fairly compact way.

You could write X, codomain(X), and possibleValue(X), but this would be pretty verbose.