orthography - How should I write my name with an American first name and Japanese last name?

I generally understand that proper Japanese uses Hiragana and Katakana is for slang/foreign words. Given that, my first name is super American but my last name is Japanese. Would I then make my first name Katakana and last name Hiragana?

(I haven't touched Kanji yet, so let's just stick to those two for now!)