I don't really like
Billy, but that is a personal pref.
Though, I could get behind it if it was short for Billina... on a girl. (Wizard of
Oz ref.)
I think if you used another
Will name, you could argue for
Billy... though I don't see why
Willem would be better than
William.
Wilhelm though - that carries a little sparkle. I like the name, but think
Billy would bring it too far down to earth for me.
Willoughby,
Wilfred and
Wilbur might work too.
I wonder if you could make something like
Jubal work? Jubilation as a noun-name might work too.
In a note of humor, my first thought was to suggest
Bilbo, ala Baggins ;)