Unfortunately you can't label a zone, but you can drag the zone stamp outside of the zone.
However you can only have one zone stamp per zone.
You can do the same with a fill and turn on the area text option.
Or I would look at setting up a schedule to show the area you want.
The schedule can't be placed directly on the plan (which is the biggest problem).
But it can be placed on the layout page so you will see it there.
I set that layout page to the trace reference of my plan so I can see the areas and the extent of my drawing page as well as any schedules I want on that plan.
One of the forum moderators.
Versions 6.5 to 25
Dell XPS- i7-6700 @ 3.4Ghz, 16GB ram, GeForce GTX 960 (2GB), Windows 10
Dell Precision 3510 - i7 6820HQ @ 2.70GHz, 16GB RAM, AMD FirePro W5130M, Windows 10