[This post was updated by moderator in 2020 to reflect a name change - deposits are now called transfers.]

you can link whatever account you want to Square for transfers as long as you have access to it.  It may not be wise both from a tax ramification and access issue to deposit to accounts that are not in your full control even if it is your girlfriend's or another family member.  Personally, I would just wait the less than 24 hours for the next day transfer to your regular bank account to avoid issues and save the additional 1% fee.