If it is healthy and cut at the proper height it will fill in by itself over time. I wouldn't bother with seed. Zoysia likes to be cut relatively short. Do not use the highest setting on your mower.

Most of the Zoysia grasses are hybrid and there is no seed, the plants are sterile like Bermuda grass. Take care of it, and it will replace itself.

Zenith zoysia is the only one available as seed. It looks very close to Meyers and El Toro (both hybrids = no seed)

If you are thinking about overseeding with a cool season grass for winter color, I'd highly suggest that you leave zoysia alone and not overseeded. It's such a dense grass that overseeding is next to impossible, and not to mention supression and rob of nutrients the cool season grass is going to do in the Spring.

If it was Bermuda, then yes. You can mow bermuda down to the sticks/dirt, then broadcast the seed for nice results.

Can you post some pictures of you zoysia lawn?

Zenith zoysia is the only one available as seed.

Add Compadre to that list.

Could it be the same grass under a different name?

Like Cavalier Zoysia and Emerald Zoysia? Both look the same...

Auteck: It is a violation of the Federal Seed Act to mis-label seed as to variety name. Zenith and Compadre are distinct and different zoysiagrass seed varieties. You should notify the US Department of Agriculture and the proprietor of the original variety whenever you have proof that a seed variety is incorrectly identified.

Here's the thing with zoysia seed. You can find it at most bigboxmarts here in GA. But it needs exposure to bare soil and full sun. The slightest little thing will shade it out. Its very finicky and difficult to start from seed. Vegetative propagation will give you less gray hairs.
You don't overseed it to fill in bare spots since it's a creeping grass that will fill in on it's own with proper care.

Quirky: With regard to your comment "The slightest little thing will shade it (zoysiagrass) out.", I respectfully disagree.
According to the experts at Patten Seed Company in Lakeland GA, the proprietors of Zenith zoysiagrass, zoysia is adapted to shade in hot climates, with shade tolerance superior to bermudagrass and centipedegrass, but less than St. Augustinegrass.
Gil Landry, Extension Turf Specialist at University of Georgia says, "Some cultivars are second only to St. Augustinegrass in shade tolerance. In fact, in the Piedmont area (northern third) of Georgia, zoysia is one of the best choices for shady conditions."
Growing grass in the shade is a challenge no matter where you live, but based on these recommendations, it appears to be a reasonable seed choice in the South, since St. Augustinegrass is not available as seed.