in Hindi/Urdu/Farsi, this term means 'life'; it's a term of endearment, like darling or dear.

Can you call a girl Jaan?

Suggested use of Jaan-e-Man (sweetheart) in Farsi & Urdu is for female (male to female) but also usable for male as well (female to male), so the suggested gender of Jaan is feminine but usable as masucline as well.

Can a girl call a guy Meri Jaan?

Meri jaan can be used for both genders.

@SamehSameerAhm2 do you know other nicknames?