Question: During periods of time, this acquistion or imposition of elements of Polish culture, such as the language, under populations of territories controlled, or under the influence of Poland; Jan Kazimierz Chodkiewicz, a Lithuanian nobleman, is a prime example of this act - what is it called? 
Sentence (from "Jan Kazimierz Chodkiewicz"): Jan Kazimierz Chodkiewicz (1616–1660) (Lithuanian: "Chodkevičius" ) was a Polonized Lithuanian nobleman (szlachcic).
Relevant evidence: Yes