How different are the two names, and do you have any official documentation relating to the name change?

You should normally be able to make the trip, without having to apply for a Belarus visa, by carrying both passports and showing the appropriate one at the different stages of your trip (there have been similar questions here posted by other dual nationals), but things are slightly more complicated in your case because of the different spellings (e.g., you would have to think carefully about which spelling to use in your booking). Having formal proof of the name change would probably help.