I don't know if there are any "rules" to this. With the Zerkowitz family, I have now seen it both ways -- as "Kohn-Zerkowitz" AND as "Zerkowitz-Kohn".
However, I'm opting to go with "Kohn-Zerkowitz". The family member who lived in Turzovka, Slovakia [formerly Thurzovka, Hungary] was consistently referred to as "Moses Abraham Kohn-Zerkowitz". This was done in very neat and deliberate handwriting, and his name is entered that way for each of his 10 children's birth records (b. in Turzovka between 1839 and 1856). Moses Abraham, by the way, was b. in Bytca, Slovakia [formerly Nagy Bittse, Hungary] in 1810 and d. in Turzovka in 1878. He was the son of Leopold Kohn-Zerkowitz (b. Trencin, 1781) and wife, Babette (Hoffman) Kohn-Zerkowitz (b. 1786).
Leopold was the older brother of our common ancestor, Samuel Nathan Kohn-Zerkowitz (1783-1847) who remained in Trencin. Samuel Nathan, as you already know, often went by the shortened designation of "NATHAN KOHN", dropping both "Samuel" on one end and "Zerkowitz" on the other.