How is the problem of sorting in contiguous runs called?
Gopan et al. seem to define a more general problem and call it array partitioning [1].

The goals of array partitioning are twofold.  First, we
would like to isolate in separate groups [...]
we partition an array so that each element whose index is equal to
the value of any of the vari ables in the set is placed in a group by
itself. [...]
[W]e partition each array $A \in Array$ by grouping together elements of $A$
for which all partitioning functions in $\Pi_A$ evaluate to the same values.

I have not dug into how their formal framework captures your problem and it may not even do so. Still, I think the general idea is close enough to use the word.
Come to think of it, Quicksort-style partitioning is related as well: you want to partition w.r.t. identify, in Quicksort we partition w.r.t. equivalence classes induced by some pivots.


A framework for numeric analysis of array operations by D. Gopan, T. Reps and M. Sagiv (2005) [preprint]