The links above have good stuff. If I recall correctly ... ZOMZ is near Moscow and was a subsidiary or under the supervison of KMZ. After 1962 the logo changed to something that looks like an eye with an arrow through it. I've seen this logo on a couple of Orion-15 lenses, so maybe ZOMZ specialized in unusual or complex lenses?
An old thread stated that KMZ and ZOMZ did a lot of military work and were therefore subject to higher quality standards than other optics plants. I can't swear to that. At some point ZOMZ got out of the camera business to focus on medical optics. Again this is what I remember from an old thread; I can't cite any written sources. Somebody who knows more than I do will probably see this thread soon ...
A lot of J-3s seem to have come from ZOMZ. On the old thread I mentioned earlier, 3 out of 4 J-3s on the thread were built there. Mine is a '61 from ZOMZ, and it's excellent. Its serial# is 619000 ... maybe it knew yours? 🙂