I learned a bit Russian in college, perhaps the following terms will be helpful:
Grandmother = ба́бушка (babushka)
Grandfather = де́душка (dedushka)
Greadgrandmother = праба́бка (prababka) or праба́бушка (prababushka)
Greatgrandfather = пра́дед (praded)or праде́душка (pradedushka)
Also as far as I know the Russian like to give Nicknames to their loved ones. Usually they do this by putting a suffix to the name (there is a rule, depending on the genus of the noun there are several possibilities), sometimes they change even more. I think it is easier if I give some examples:
Jekaterina could become: Katja, Katerina, Katetschka, Katenka, Katjucha, Katjuscha, Katka
or
Pjotr could become: Petja, Petenka, Petruscha, Petjunja
Names often are changed so much it is difficult to recognize the real name behind it if you aren't a native russian. (At least I feel that way)
Even lifeless objects are getting nicknames: "dom" (house) becomes "domik" or "oblako" (cloud) becomes "oblatshko".
Wikipedia has a page about
Diminutive which includes several languages, perhaps this gives you an idea for the nicknames.
