I have an iMac and a Macbook Pro. Both worked fine with AirDrop but one day got out of sync. To fix the problem, I went into System Preferences | Users & Groups, then clicked on the Change button adjacent to the Apple ID section. I entered my system password, when prompted, clicked on the email address associated with my Apple ID, and then clicked the "minus sign" button to remove my Apple ID. Next, I clicked on the "plus sign" button, entered the email address and password associated with my Apple ID, and tried AirDrop. It worked perfectly.
Keep in mind, this is the same Apple ID, used on two different systems. If you can't get it to work, I'd suggest removing and re-adding it to one system and trying it, as stated above. If that doesn't work, try to remove and re-add it to the second system.
DG