Maybe because there is music theoretical reason not to name h with b?
Or because every other musician you are dealing with thinks a b is hes?
Well, actually, every musician I know would be most confused on
finding the note h in a score. Maybe like me they know the dual
notation, but I didn't know h was bes - to me it's b.
I don't think it was implied that h equalled bes - of course it's the
other way around: In languages where the semitone below c is called h,
oftentimes b means hes.
After all, i play a Bb instrument, and I'd be EXTREMELY confused if
someone referred to it as a B instrument!
In English, yes, that would be very uncommon. In German, for example, we
say "B-Trompete" for a Bb trumpet.
The historical reason is a bit confusing: In fact the ambiguity is
already baked into the tone system in Guido of Arezzo (Micrologus of
~1025) in that in the /low/ octave, he constructs [Gamma] A B C D ...
with B-C a semitone. In the /next/ octave, he constructs F G a ♭ ♮ c
where ♭ is our modern b-flat and ♮ is our modern b-natural. Of course, ♮
became "h", but in fact, there's precedent for both conventions in that
very old system.
Lukas