They're not straightforward.
There is an "official name" and it's on your registration certificate.
The thing about official names is that I have so many to choose from! Alien registration certificate? MCKENZIE PATRICK JOHNATHAN. No kana because town hall called up the local immigration authorities and heard "'Nicknames' are not required for the administration of Japanese immigration law and accordingly should not be registered. You should only register him under the exact name printed on his passport." (This is official policy, but many local government authorities ignore it, including half of the clerks at Ogaki. I drew the short straw on my most recent visit though and "had to change.")
Mr. Short Straw did not, however, actually use the name written in my passport, because some genius at the US Passport Control Center thinks Irish people get an extra space in their last names and, after substantial argument with town hall, I was able to convince them that a lifetime of being addressed as Mc-san would be very inconvenient for my wife and I.
But wait there's more! As a result of marriage the McKenzie household finally exists on the books in Japan as a 戸籍, whereas before it was just little ol' me happily residing here as a foreigner. An hour of investigation with a totally different part of the Ministry of Justice later, Town Hall refused to register a 戸籍 with Latin characters, and was actually able to produce an authoritative Least Frequently Asked Questions At Ogaki City Hall internal guidelines document on what to do in the event of international marriages. So my "official" name in that part of the system is different: ミッケンジー、パトリックジョナサン. Mr. Short Straw remarked, direct quote, "Cripes, that seems like an inconvenient name to go around with. Have you considered just changing it? I've got the forms and I'm pretty sure you could be Tanaka Taro by the end of today." (Bonus points: We filed a name change for Ruriko at the same time as getting married, and hers is based on what's written in the 戸籍 and her 住民票, which gives us the wonderful circumstance where "Wife took husband's name after marriage but, important note, their names will still fail naive string compares... well, some of the time, depending on which agency and what data source we're querying.")
But wait there's more! City Hall is my single point of contact for Japanese Social Security, Japanese national insurance, and the Gifu prefectural revenue office. I think I count four different official names there unless one or more decided to change policies recently. Gifu extends its apologies but it is physically incapable of handling sole proprietors with given names which are 7 letters long because, quote, "Who does that to a child?!", so Kalzumeus Software is on the books as being owned by MCKENZIE P.