At this point I'd say that although there are the certain neighborhoods in NYC (China Town, Little Italy), they are currently pretty diverse, even the ones that are known as Dominican neighborhoods or Puerto Rican ones have people who are not that ethnicity.
I'm not going to tell you what to name your characters because I think it's your job as author. I do want you to think about your who your characters are and who their parents (who named them and gave them their last names) are.
If I were to write a story about me, I'm a western-European mutt. However, I strongly identify with my father's mother's ethnicity even though that's only 1/4 of who I am. This side was the latest to get to the US. Does this mean that no one can relate to me as a character? My last name (same ethnicity) and grandma's history is so insignificant in my relatability because it's how I'm written that matters. However, I do celebrate that ethnicity at Christmas so it's not irrelevant to who I am.
There are more Slavic naming conventions other than -ov/ova or -ski/skya. A prime example is Novak.
Also, (this is nit-picky and you clearly can take it for what it's worth) I don't know how far away from the old country Tzar's parents are, but here's something I picked up from living in Slavic countries. The Slavic /c/ pronunciation is written as ts and not tz. The title of tsar is derived from the imperial title Caesar and the Russians literally transliterated the letters so they used Ц, which is the /c/ in non-Cyrillic letter Slavic languages. So seeing Tzar shows me that the family isn't that aware of their heritage.
~Raging and quivering female mass of hormones and tosser of Dark Side Cookies™ (trade marked by Etoile)