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... at least in Hungarian, -ka, -ke are diminutive suffixes, while the -i ending, just like in English, is a sign of the pet form.

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So if we suppose that your name is of Hungarian origin, it could come from Natália (Natalia) or Natasa (both are legit full names here) shortened to Nati, plus adding -ka for diminution.

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But note that this is only a possible origin, it could come from a different source as well...