Correct term for a priority queue with unique elements
I don't know of a name for the abstract data structure.

There is a well-established implementation of what you describe, though: treaps, a combination of BST and heap (i.e. priority queue). This is with priority and value/key being different things, though.

If priority and value are the same, use any priority queue and add uniqueness, i.e. by combining it with a set/dictionary data structure. (Treaps degenerate to sorted lists in this case.)