I have a hose reel where this one piece has broken.
I literally can not come to spend another $100 on the entire assembly when all that's broken is this piece, but I don't even know what to search for in this case.
Our big-box stores definitely don't carry it.
It allows the assembly to spin (for reeling in, and unreeling)…
This is where it goes:
Best Answer
A swivel or "rotary union" (but there are many things under the same names that don't look like that, or in some cases work like that. It's imprecise, but does cover what you have, as well as some other things.)
Specifically one with one side "garden hose thread" and the other appears likely to be pipe thread in a smaller size.