The mannequins are given to you by Sable, Gracie, and Labelle. You can't drop them on the ground, however, so nobody can give them to you. Sable gives you her mannequin when you talk to her for a certain amount of time, Labelle gives you hers when you buy a certain amount of items from the Able Sisters, and Gracie gives you hers when you buy your first item from T&T Emporium. Hope this helps!
Sable's mannequin is obtained by becoming best friends with her. The player must also have purchased at least 50 items from the Able Sisters shop. The earliest this mannequin can be achieved is by the tenth conversation with Sable.
Mabel's mannequin is obtained by purchasing 51 clothing items in the Able Sisters shop.
Labelle's mannequin is obtained by buying at least one accessory from her a day, over 31 days. The purchases do not have to be made on consecutive days.
Gracie's mannequin is received when the player makes their first purchase on Gracie's floor of their own T&T Emporium.