Would the person who dumps the dumper also be called a dumper, or rather a dumpster?

Let’s say a person who is sick of their partner decides to dump them.
Is the one a dumper because they can’t live up to the expectations of the other, and the other a dumper because they dump them?
Or is the gender important to answer it correctly.
Can a dumper/dumpster be all genders?
Who dumps who (and what are they called then)?