For me, art style won't bother much if it's anime-ish. Anime has covered almost every major cartoonish nationality from Japanese, French, American to some minor ones like Egyptian, Indian and even Thailand and Laos. The style is rather universal, so any name should fit. The more important aspect toward naming is how you handle the names and relate them to the characters themselves, the audiences, and how the characters are depicted within the setting.
Characters with common and easy-to-remember names like John, Bennett, Smith, and Alice are subjected to be more relatable to the audiences and real life society. Nick Carraway, for example, is supposed to be a reader surrogate and an everyman, so the name is really fitting and memorable. Common names also make sense you in a setting relatable to real life and society. You won't see a lot of characters named Artemis or Orden in the present day sci-fi and horror movies, but rather Dr. Smith and Harry Mason, for instances.
On the other hand, using special names would help signify the characters being special and important to the plot in certain ways. Characters with strange names, but not too strange, tend to be memorable and iconic: There's only each one of the famous guys named Rinoa and Sephiroth in gaming, for example. Authors also like to like the name with the character's traits: Sonic the Hedgehog is named because of his speed. Mile 'Tails' Prowers is named because of his two tails and his tendency to fly around for a long time. Fuujin and Raijin are named with the words in sync, implying they will always appear together as a pair. In my case, I name one of my characters 'Caius' because he's supposely the happiest kid in town.
Characters with 'minority' names and appearances in gaming tend to be something of an appealing factor. The names signify the uniqueness of the characters compared to the others. Japanese characters in European theme-JRPG are usually the result of the authors wanting to insert the iconic historical stereotypes into the games. It's a fanservice to the nationalists that way, and you know how nationalist Japanese people are. I myself plan to have an ancient Thai swordwoman in a Norse mythology-based futuristic world, and I won't even care how clashing it sounds.
*edit* About the Japanese names, be sure to check if the words have the alternative kanji writing. A lot of words in Japanese and Chinese have multiple meaning based on how they are written.