I almost feel I can't find any Japanese influence on the KH series (due to my own flawed POV) D:
I mean, the entire series has a Japanese influence because it was made by Japanese people. The fact that it's not always overly obvious with big neon signs doesn't make that any less true. Similarly, everything I write has a Canadian influence because it was made by me, a Canadian, who grew up in this culture, but that doesn't mean that everything I write is going to have Aboriginal folklore in it or reference hockey or Tim Hortons or the existential dread of living on the Prairies. Doesn't make it any less Canadian though.
That being said, I don't know what you're focusing on, but the KH series has a lot of clear observable Japanese touches and references to the culture.
Everything about Destiny Islands' island culture is very much based on Japan, even complete with the school uniforms. The names of Sora, Kairi and Riku, as already mentioned, also clearly bear this influence and touch. Twilight Town as well is also pretty Japanese with low-sitting beds, an emphasis on public transport, one month vacations (which also extends to other series characters' like Axel who believes this too despite growing up in an entirely different world), etc.
And of course there's TWEWY's inclusion, with Shibuya and the characters being very obviously Japanese (though one can argue that all OCs in KH are coded Japanese, too).
Some of the most obvious is with BBS and TAV. Proper Keyblade teaching and culture is very clearly samurai-inspired, with pretty much all of the main characters having Japanese-style clothing in their outfits (Aqua's kimono sleeves, Terra's hakama pants, Eraqus'... entire character design basically lol).
Other influences that people have mentioned are of course KH2's more shonen bent, the cultural context behind Sora bowing to Saix, and the designs of certain Keyblades.
Some of this stuff is lost in the localization of course such as the fact that dialogue in the original Japanese games use honorifics, which are completely removed when localized. One such example is when Donald chastises Sora in KH2 to "show some respect" when meeting Yen Sid. In addition to Sora not bowing, Donald is also chastising Sora for not using the proper honorific to address Yen Sid in the Japanese version.
Some of the Organization weapon names in 358/2 Days are also references to Japanese culture.
Many also believe Riku's haircut in DDD to be a sign of Japanese culture as cutting one's hair like that is often considered symbolic of starting a new journey and leaving the past behind.
Translator Goldpanner has also stated in the past that the way Kingdom Hearts X is written is very much in the style of a Japanese Fairytale, and that she believes that is one reason why the dandelion imagery is used so extensively in the game.
Those are just some of the instances off the top of my head, I'm sure there's many more as well.
But, you know, Disney themselves have said that they consider the core themes of the series revolving around the heart as very "Eastern thinking", and that's what the entire series is based upon. The series also puts a great deal of emphasis on the importance and good of collectivism and of people coming together and supporting each other in order to become strong and the like, which at times directly contradicts more Western thinking that proclaims individualism to be the highest order (it's no surprise, for instance, to see many fans react strongly to Xigbar's lines in KH3D (and Kairi's in KHII) that Sora is only strong because of the people he connects his heart to). I would say that is probably the biggest influence as it is the foundation for the entire series.