The question (not mine) was not what your name mean, but why did you choose it! Do we have something to learn from appeasement if we infuse some yeshiva enthusiasm in it?!
Earliest Chaim Berlin was named so in 1914 when Mr. Cham Berlain was already an adult, so he did not attend the yeshiva. So, most likely Mr. Cham Berlain was named after the _original_ r Chaim Berlin, son of Volozhin RY. This is also cler from the fact that Cham Berlain was a Mayor (Meir) of Birmingham, while Chaim’s brother was named Meir and also partioned his name from BerLin to Bar Ilan.