Pick a name. Pick a period.
https://sengokudaimyo.com/japanese-names provides a good overview of how names work and includes some examples.
Name Construction in Medieval Japan is pretty much the go-to reference on Japanese names for SCA use - and you won't have to photocopy pages when you do a name submission.
Amazon currently has it available. Alternatively, contact a herald in your kingdom – that’s what they’re for. Or ask for help or the SCA Japanese Facebook group.
http://cunnan.lochac.sca.org/index.php/Japan isn’t a bad overview (though I spotted an incorrect date in my cursory reading). Use it as a springboard to do some reading if a particular period sounds interesting to you.
Acquire a vocabulary.
There are two reasons for this. First and most importantly, it’s hard to search for information on something when you don’t know what it’s called in Japanese. Don’t be afraid to ask for help on the Tousando or SCA Japanese Facebook group. Someone else may know the answer and then you will know those fingerless glove-like things you saw someone wearing in “Princess Mononoke” are called tekkou. Acquiring a vocabulary in a foreign language takes time – and your web search will fail if you get the spelling wrong and go looking for “kasoda” instead of “kosode.”
Second, no one in the SCA expects anyone to say hello in Middle English or Old Norse, but if you have a Japanese persona, people think you automatically speak some Japanese. I have no idea why, but they do. Shikata ga nai.
A few greetings, yes, no, please and thank you, are nice to know and will add flavor to your persona impression, but they are *NOT* essential. (Besides, it’s modern Japanese anyway, right?)
Armor glossary: https://sengokudaimyo.com/katchu/katchuch02
Women’s clothing glossary: http://wodefordhall.com/page3.html
Men’s clothing glossary: http://wodefordhall.com/page2.html
Textile embellishment glossary: http://wodefordhall.com/page13.html
Google Translate: https://translate.google.com/
RomajiDesu Japanese Dictionary & Translator: romajidesu.com
https://www.coscom.co.jp/learnjapanese101/wordcategory/basicwords_greeting.html has a nice selection of modern Japanese greetings, including sound files so you can hear how they are pronounced.
It helps to know the basics when exploring Japanese words rendered phonetically in our alphabet, a system known as Romaji. http://iprc.soest.hawaii.edu/users/furue/jp-pron.html
Acquire the mindset.
Read literature from your chosen period. If your persona was kuge (aristocracy) or buke (samurai), they would have been literate and likely to know classic poetry and tales as well as being able to write a bit of poetry. (See bibliography.) Even a peasant, merchant or artisan would know folklore.
The Japanese were – and still are – very status conscious. How one greets another is fraught with measurements of status. Know and use the appropriate honorifics when you can, particularly with other SCA Nihonjin. Most people recognize “Name”-san, but it’s relatively modern. “Name”-dono is an excellent gender-neutral honorific. It translates as “lord,” but you can use it with anyone. When in doubt it’s the perfect default!
Acquire the trappings.
This seems like a lot and can be overwhelming, particularly as SCA merchants rarely have anything that’s appropriate. Take a deep breath and remember that the only requirements for participation at an SCA event is make an attempt at pre-17th clothing and behave like a lady or gentleman.
Take it in stages as your time, budget and skills permit. Resources exist. Try your hand at making the things your persona would wear or use if you like making things. Barter skills you have for those you don’t.
Even by starting small, you can build towards your wow-factor dream kit. Do your homework, learn what period clothing, armor, etc. are supposed to look like. Aim high!