If we assume the standard model falls into 3 generations ordered by mass. (This needn't necessarily be true.) We call these "generation 1", "generation 2" and "generation 3".
So the property of a muon belonging to generation 2 we might call it's "generation-2-ness". This is far from ideal.
Are there any better names for the quantum number referring to a particles generation?
Maybe "e-ness", "mu-ness" and "tau-ness"?
If for example there was discovered a force like $SU(3)$ which acted on flavour, it would be nice to have better names for the generations. Just like with chromodynamics we have red, green and blue.