It can't, because it's but a bot, and quality of the sources used as a seed sequence for its hallucinations leaves much to be desired. In this case, the surname is neither: not Anashin, not Anashinkin, but Anashkin. Russian surnames change according to rules of declension, but roots and suffixes are constant. Only endings vary. Ending may be null, as in nominative case: Anashkin. In other cases, ending is glued to the stem structure: genitive Anashkina, dative Anashkinu, accusative is formed just like genitive, instrumental Anashkinym, and so on.

Declensional endings also depend on number, gender, and animacy.