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Last name origins & meanings:

1. Jewish (eastern Ashkenazic): habitational name for someone from any of various villages called Berez(i)no, Berez(i)na, and Bereza, in Belarus and Ukraine, all derived from an Eastern Slavic noun meaning ‘birch tree’.
2. Russian: topographic name for someone who lived by a birch tree, from Russian bereza ‘birch’ + the Russian possessive suffix -in.