Taganrog is not formally a brand. It is more the name given by in-the-know consumers to a set of derailleurs that were possibly manufactured unofficially by Yakov Dmitrievich Bordyugovsky in the 'Taganrog Aviation Scientific Technical Complex named for G. M. Beriev' (Таганрогский авиационный научно-технический комплекс им. Г. М. Бериева). Georgy Mikhailovich Beriev was the Soviet Union's foremost designer of flying boats, and the Taganrog Aviation Scientific Technical Complex (which was created and managed by Georgy Mikhailovich) was the Soviet Union's foremost builder of flying boats.
As you might have guessed the Taganrog Aviation Scientific Technical Complex was based in the city of Taganrog. Taganrog is in Russia, situated on the Sea of Azov, just across the border from the criminally destroyed Ukrainian city of Mariupol.
Yakov Dmitrievich Bordyugovsky worked in the flying boat factory and seems to also have had a parallel existence as a cycling coach. In the Soviet style, he appears to have availed himself of the chronically underused skills and resources of the aeroplane factory to manufacture a line of rather classy derailleurs. I believe that the term is 'samopal' (самопал), which kind-of means 'home made'. But 'home made' has an amateur, country cottage feel. 'Samopal', in contrast, may also incorporate the idea of illicitly using your employer's latest and hottest technologies to craft something you can sell privately, rather than wasting all that amazing capability in the diffident pursuit of irrational targets spelled out in an incomprehensible 5-year plan.
It is possible that Yakov Dmitrievich Bordyugovsky started his, rather laudable, scam in 1976 and continued up until the collapse of the Soviet Union in 1991. Even today, you see Taganrog derailleurs surprisingly often, indicating that they were manufactured, at least, in their hundreds and possibly in their thousands. This was not a small operation.
The Taganrog derailleurs are often found fitted to Tachyon bikes, and so are frequently referred to as Tachyon derailleurs. This is incorrect, Tachyon derailleurs are something quite specific and quite different from the Taganrog designs.
Finally there are various legends about Taganrog derailleurs being made out of surplus super-high-tensile helicopter blades, or being manufactured in Magnesium or Titanium. As far as I can tell they are machined from billets of some kind of respectable aluminium alloy. They are often finished in a distinctive, undyed, hard-anodised, 'antique bronze' colour. I am told that this very tough, but rather unattractive, finish is typical of many components used in the Russian and/or Soviet aerospace industry.