This comment claims that Sulu is not a Japanese name (technically true), but I always assumed that Gene Roddenberry intended the name to be Japanese but he was just oblivious or ignorant. It certainly seems to me that Sulu conforms more to Japanese phonology than any other language or region[ citation needed :) ].
So if we ignore the issue of the name itself, what is the actual earliest evidence that Sulu is Japanese?
In Star Trek VI: The Undiscovered Country we learn that Sulu's first name is Hikaru, which is a name of Japanese origin.
In the story "The Squire of Gothos", when Trelane meets DeSalle he speaks French to him and then when me meets Sulu he greets him in Japanese.
If you're looking for out-of-universe evidence, I recall George Takei saying in an interview that Sulu was supposed to have a Katana in "The Naked Time." But Takei requested it be changed to a European sword as he was "Japanese-American" and didn't want to portray himself as traditional Japanese.
Of course, it could just be that "Katana" was the only type of East-Asian weapon known to Roddenberry or the production crew. But I believe it is uniquely Japanese.
I think it was from the special features of the first Abrams movie when they're discussing new Sulu's ridiculous folding sword and its continuity (or lack thereof) with classic Sulu's European fencing sword from The Naked Time.
I'm trying to find a source.
EDIT: found a source, although it's not the one I originally remembered this from.
John D.F. Black came up with Sulu's "berserk" scenes without specifying the weapon to be used. Unable to decide between a samurai sword or a fencing foil, he left the choice to George Takei, who picked the latter with the thought that by the 23rd century Humanity would have developed to a point where, in terms of culture, people have moved beyond simply adhering to ways of their ethnic background.
From Memory Alpha, quoted very closely from this video. The fact that Sulu argues that culture shouldn't just depend on ethnicity leads me to believe that the actor's ethnicity was taken into consideration when conceiving the character.
I still recall a different video in which Takei explicitly draws a line between being "Japanese" and being "Japanese-American" which I think makes my case more convincingly, but I can't seem to find it.
If I recall correctly, there was a book in which Sulu was initially assigned to the Enterprise under Kirk and he was protesting that he wanted to be assigned to a patrol ship near his home planet of Gaijin which was under some sort of raider/pirate pressure. I seem to recall it had a story line about some sort of acting group onboard and the Klingons were also involved. Gaijin is a Japanese word - though it means roughly "foreigner" which is kind of strange for a name.
