John / Jonathan: two distinct names.

Jonathan:
from jo - nathan, Hebrew for "God gives"
(related to Nathaniel, which is nathan-el = "gift from God")

John-with-an-h is indeed analogous to the German Hans / Johannes but comes
from jo - khanan, Hebrew for "God is merciful"

(Been there, done that. I have a son Jonathan; we've seen all kinds of well-intended alternative mis-spellings: Jonothan, Jonathon, Johnathan, Jhonathan, etc. )