I have received a gift from a foreign person, and I know I need to file form 3520. However, on the form, do I need to put my Husbands name as well, since we are filing jointly ?

Or does my name only go on there since I was the one that received the gift and not him ? Also, do I need to put his SSN on there also ? And who signs it, just me or both of us ?

If the gift was ONLY to you, then ONLY your name and SSN goes on the Form 3520, with only YOUR signature.