I am a Russian-born American citizen who grew up with an American passport and recently obtained a Russian passport because the Russian government changed the rules about citizens with dual citizenships getting Russian visas. Took me 8 months to get the Russian passport. Only to find out that the surname spelling is off by 4 letters. Both names are pronounced exactly the same in Latin script.....but look completely different.
Are you surnames COMPLETELY different or are they just slightly off like in my situation? Buy the plane ticket in the Belarusian name. Show your Belarusian passport at all stages of the trip. When you check in for your flight back to the Western Hemisphere, show both passports at check-in. I had no problems flying with Lufthansa through Frankfurt.
Good luck!
If, however, the names are completely different, I would get official documentation of said name change. It couldn't hurt.