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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!)
Foreigners's names are usually written in katakana, even when their names are based in Japanese.
For example, Michio Kaku is a Japanese-American with a full Japanese name, and yet his name is usually written in katakana.
https://ja.wikipedia.org/wiki/ミチオ・カク
Other examples:
https://ja.wikipedia.org/wiki/日系アメリカ人の一覧
But if you are living or wants to live in Japan you can adopt a 通称名, a name to be used inside Japan.
Then you can adopt a name in kanji, if you want to. You can for example change Higa to the original kanji name.
If you live in Japan, I think it would depend on your nationality.
If you are a Japanese national, then you may use the Kanji surname in official documents because that is how it's supposed to be recorded in your Family Register (called 戸籍{こせき}), unless for some reason it was purposedly registered in Katakana, which is kinda strange if one of your parents is Japanese.
If you are a non-Japanese national, it has to be in Katakana in official documents. If you still want to use Kanji, you may after you register a legal alias (called 通称名{つうしょうめい}) in the municipality that you live in, but there could be limitations to its usage.
For non-official documents, I don't think it will be a big issue if you use Kanji, but then it might be confusing later on to remember which name you used where.
I tried to look for official (Japanese Government) sources in English but couldn't find any. You can get more information from below references:
