Quote Originally Posted by TATY
Am I right in thinking that the letter Й was added to these names of foreign origin to make them declinable?

E.g. if they left them as Григори and Георги, the names wouldn't decline.
No, I don't think so.
There's a very common tradition: many of the greek/latin words ending in -os, -us, -um get endings like '-ий' in Russian. This is true not only for names. For example, most chemical elements are translated this way: "Lithium" -- "Литий", "Rubidium" -- "Рубидий", "Plutonium" -- "Плутоний", etc.