There is another "westernized" name pronunciation in the game, too.. I doubt any Russian (Vlad) or Serbian (Niko) would pronounce the name Ivan as "aye-vin" rather than "ee-von." I don't think Rockstar was stupid enough to miss the fact that it would be pronounced "Belich" though, I'm sure they have their reasons for keeping it as "Belick."
Also as for the accent, you need to give the guy a break. Niko is voiced by Michael Hollick, an American who I believe is from the east coast. He pulled off the accent pretty well, and although his Serbian lines sound a little forced, it's not really that bad.