Is there a name for this priority queue data structure?
This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:


You have fast set and get at any index
You have fast "aggregate" queries on ranges
You can support fast update queries on ranges, for some combinations of updates and queries


The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(\log n)$ time.

The range queries can use any associative operation. In your example the operation is $\max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).



I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).