But if Bulgaria had a  large separate ethnicity of Roman Catholic faith as BIH. Which ethnic identity Orthodox Bulgarians converted to Catholicism would adopt eventually? From my observation they’d likely to adopt identity of the Catholic ethnicity as in BIH or western Belarus/eastern Poland.

Our Lutherans kept Belarusian identity. Not German or Latvian. In eastern Prussia many Poles and Lithuanians who were Lutheran adopted German identity. But not all of them. Mazurs (Lutheran Slavs of Polish descent) for example considered them a separate ethnicity from Poles.