Where does “Jan” come from?

Jan is an English shortening of Jane, which derives from the French feminine suffix -e applied to a form ultimately from Hebrew יהוה via Ancient Greek Ἰωάννης.

Ancestry of “Jan”, step by step

Step	Language	Word	Meaning
1	Old French	Jehan	John
2	Latin	Johannes	John
3	Ancient Greek	Ἰωάννης	—
4	Hebrew	יוחנן	Yahweh is gracious
5	Hebrew	חנון	gracious, merciful, compassionate; passive...
6	Moroccan Arabic	خنونة	mucus, snot
7	Arabic	خُنَّة	—

Every word from Arabic خُنَّة →Every word from Moroccan Arabic خنونة →Every word from Hebrew חנון →