I am usually asked for my "numero de documento" when making a purchase with a credit card or an item with a guarantee.
My Argentine girlfriend always used the word "documento" when referring to her DNI (as well as my need to have one).
So did the police when I made a denuncia, the excribanos at my escrituras, the folks at AFIP when getting my CUIL, the art appriaser at Banco Ciudad, the agents at the aduana when getting the permit to export art, etc.