I don't think it's Russian. I can't find anything about Borat being a real name, but the -at ending makes it sound like a name from a Turkic language (and Kazakh is part of the Turkic langugage family).
For example, this site (in Russian) has some Kazakh names on it:
http://www.kazakh.ru/about/name/ There is no Borat or anything similar to it, but several with the -at ending: Azamat, Azat, Askhat, Akhat, Bekzat,
Murat, Samat (all male),
Bakizat, Gul'shat, Zumrat, Kayrat (all female).
For most the origin is given as Arabic, for some Iranian (Persian would be more correct).
Maybe Baron Cohen made up a name, modeled on existent names of that region. If it does exist, it might be related to
Bora (Turkish name), but that's just a guess - and a veeeery long shot.
*****This message was edited 11/29/2006, 5:28 AM