The name of Kozina the famous rebel was really Jan Sladky. He lived in Ujezd u Domazlic in the house who called " u Kozinu". He was also called by house Jan Sladky-Kozina.
It can be that your Kozina ancestors were from another village of Chodsko region.
My wife has the family Kozina between her relatives.
Contact me directly to: a.kondry(et)volny.cz
All the best. Tony.