Umm...its not so clear-cut:
There is, of course, Genrikh Moiseyevich Kasparian who was born on the 27th of February 1910 in Tbilisi, Georgia. The famous chess composer.
And there is Garry Kimovich Kasparov, born as Garry Vajnshtejn (the surname analogous to German "Weinstein" ) in Baku, Azerbaijan April 13, 1963.
However, after Kasparov's father died (Garry was 7 at the time) but as soon as was legally possible (at the age of 12), Garry
adopted his mother's surname, Kasparian. Which he, however, modified the name to a Russified version - Kasparov.
So, he was born Vajnshtejn (or Weinstein) then changed to a modified version of Kasparian, which is the famous Kasparov.
So, although I've never actually seen someone reference him as Garry Kasparian..its not completely unfounded; though its also not completely accurate either since Kasparov himself chose to modify the name and he presumably never went by Kasparian.
Personally, I'd stick to "Kasparov" since that's the guys legal name and also what his friends call him.
{Not to mention it could become a bit confusing with two famous Kasparians. Sort of like Ed. Lasker and Em. Lasker.}
But technically, I suppose
both Smyslov_Fan and Dragan Glas are correct. Just thought I'd share.
Cheers,
Nietzsche
PS - A rose by any other name would still dominate chess for over 20 years, achieve the highest career rating of all time, and defend his title like a real champion...