Legal name changes for JP-US dual citizens

I'm a Japanese-American dual citizen residing in the United States right now, and I'm expecting to legally change my name in a Californian court later this year, and then changing my American SSA and passport names in the United States. Once I've sorted out my American documents, I'm expecting to return to Japan and start the process of legally changing my name on my Japanese documents, as well. The name change is for gender reasons. How should I start preparing for the name-changing process, if I can? What documents will I need? (I'm expecting to have my American documents reflect the name changes by then, so I'll have proof of a name change by an American court.)

the law application for gender problems may differ between USA and Japan. probably, you need to consult a lawyer.
in general, if you want to change your name, you should go to a family court. but, you want to change your sexuality. it is not easy in Japan.
moreover, the complexity may occur that you already violate the Japanese law that dual nationality holders must choose one nationality when you become 20 years old. (the limitation is until 18 years old, but you have 2 year's grace term.)

Proceed with caution. Japan does not permit citizens to hold another citizenship. You are in danger of losing your Japanese citizenship should the Japanese government find out that you are a US citizen as well as a Japanese citizen.

I'd be more concerned with what is legal in USA regards gender identity may not be legal in Japan.

I would consult lawyers in both countries first before moving forward with any changes.