On some domestic US flights I take where I am in first/front cabin, I have seen variations of both the OH bins already closed, and as you go to open them the FA will ask where you are sitting as if to bless your stowage in that section, or the FA just being proactive as soon as you go to stow it if they are already open. I have also seen them take other passengers luggage out and walk it to the back of the aircraft when they have asked "whose is this?" and if no-one identifies it in the first section/cabin they walk to the back of the plane asking the same question until someone identifies it. And if no-one does I have seen them gate-check it.