Why is XNOR gate not referred to as an "Equality" gate?
I think that's a valid observation.

The reason it's called an XNOR is that all logic gates are based on boolean algebra. The boolean operations of conjunction, disjunction and negation map isometrically to AND, OR and NOT. Combining negation with conjunction and disjunction gives you NAND and NOR and exclusive disjunction gives you XOR. Naturally then, when you add negation, you get XNOR (which is simply easier to say than NXOR).

The fact that XOR performs an inequality operation and XNOR performs equality operation is a by-product, but a valid one nonetheless. Note that it is no more remarkable then the fact that AND is modulo two multiplication and XOR is modulo two addition. You're free to use the representation that is most convenient to the task at hand. If you're programming, then converting your result into arithmetic operators makes sense.