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:
- https://www.japan-guide.com/forum/quereadisplay.html?0+162645
- As a foreigner with a Japanese name, what are the implications of writing my name in katakana or kanji?