Privately, and I do *not* need y'all spreadin' this all over, by 507ce the western roman empire was quite over.
The two closest things to a western roman emperor were Odoacer and Theoderic. And they were *very* close to being that, a fact they both were rather well aware of, drawing mightily on the trappings of Roman imperial history. Further, they even both sustained the people of "Rome", tho mostly from the loving distance of Ravenna.
However, neither of them were de jure.