Union there was any marketing. Is it a logo or special trademark? To understand, whether there were other brands at the same plant it is necessary to dig more deeply.
So so far we will call them logos and I will describe here what I know and which I met.

Summary
– KMP (Krasnogorsk Mechanical Plant)
– Arsenal plant
– MMP (Minsk Mechanical Plant)
– LPOG (Lytkarinsky Plant of Optical Glass)
– Valdai. Valdai Optical-mechanical Factory

The subject of the Soviet lenses and cameras is quite extensive and first of all thanks for that to Germans (engineers, not politicians), the equipment and drawings we used after war. In the first decade even it was possible to make quite worthy cameras and lenses. We are obliged by the lag in this area still to imperial Russia which wasn’t guided by technical progress and the mentioned jump in production of photoequipment could be aproached only by involvement of the German personnel of Carl Zeiss plant on account of reparations, receiving from them detailed drawings and the help in adjustment of lenses production and cameras.
A bit later I will add a table of correspondences of the Soviet and German lenses to the article. There were used different fastenings of a lens: M42, M39, Nikon of F, Leica, etc.
Machines, spare parts, glass were so taken out and involved the engineer from Carl Zeiss to adjustment of production at the Arsenal, Kiev plant. Here one product sample (Kiev-4) with the picture of a prototype (Contax-D).

Contax D

At first spare parts were delivered from Germany. On a photo a metal slip from Contax, outside at it it is written Kiev-4, and inside there was Contax engraving.

metal slip kiev4 contax d

AND NOW ABOUT LOGOS

KMZKMP (Krasnogorsk Mechanical Plant) is known for high quality production among other Soviet optical plants. It released so well-known cameras as the Zenith, Sharp-sighted, the Horizon, Moscow.
In the oldest version of a logo there was no the beam passing through a lens. Such logo was used about approximately in 1950 year on the FED cameras.
The second option was used for 30 years and it is most known. The third option of a logo was approved at the end of the 70th and is still used.

Arsenal plant

logo arsenalThe Arsenal plant is in Kiev, in Ukraine and is known for its copies of cameras: Hasselblad, Contax, Nikon and Pentacon Six. Some of them were completely copied, but the device was simplified for production reduction in cost, but some (such as Contax) are quite worthy copies.

MMP (Minsk Mechanical Plant)

mmz logoIt is based in the 1957 and it is located in Minsk, Belarus. I made optical glass and the Change-2 camera. In the 1971 it was renamed in BELOMO.

LPOG (Lytkarinsky Plant of Optical Glass)

LZOS logo
LPOG (Lytkarinsky Plant of Optical Glass) was in Lytkarno, in 100km to the North from Moscow. It was KMZ subsidiary. Quality of its lenses leaves much to be desired, despite communication with KMZ.

Valdai. Valdai Optical-mechanical Factory

valdaiIt is located between St.-Petersburg and Moscow. This plant was the producer of lenses for KMZ and Zenit BELOMO. Its lenses had the name Helios.