No. Arena really is what a pool allocatable memory is called.
The article claims the term first appear in V6 Unix though I couldn't tell you why it's called that.
It does help prevent confusion, though, a memory "arena" and a memory "area" don't both mean the same thing.
I'd propose "colosseum" for a really big arena such as one used by a compacting GC, and "skyrim" for a scrollback buffer (holds elderly scroll-text), but they'd never catch on.