We actually have multiple names for all the notes - which have a 'reason' to exist. A B-double-flat and an A-natural, and G double-sharp exist, distinct for notational purposes... yes, it sounds dumb. Music IS arbitrary in a lot of ways.

For example: 12 tone equal-temperament was chosen/invented (nearly) (by Bach) over just intonation because of 'musical gags' like https://en.wikipedia.org/wiki/The_Musical_Offering (also written by Bach).

Music making neat, orderly, mathematical sense is the struggle, and reality doesn't play nice with harmonics like we would like... (much like with irrational numbers throwing a wrench with Pythagoras' ideals) so stop being a Pythagoras :p

Music IS weird: no matter how you try to quantify it.