My setting is elsewhere. It made sense to name them something in the vernacular of the region. And yet, as I'm re reading my work I see I keep flipping back and forth between their Basque names and the English translation of those names. LOL. Guess I'll have to fix that eventually.
Yes, keep their culturally correct names for sure. Anything else would damage the inegrity of the story.
I intend to, I just am tryng to figure out dialog/narrative for a story that takes place in the 1100s in a town that speaks an entirely different language. When they get to France I refer to the mother character as "maman" in all dialogue. But I am itching to find some terms or phrases in Euskarie I can incorporate into the story to keep it more consistent in that setting. Also...French characters... I do it there too lol. Etienne, Steve...Jean John. Maialin, Magdalein, Mari, Marie.... It's going to be fun cleaning up this manuscript hahaha.
It wouldn't make much sense to write a book that takes place in another country and then give them names like Jane and Mike. If you're having too much trouble keeping track of your characters names, you could start using a familiar name and then when you're making your final edits, change all the names.
I would recommend writing down your character's names and descriptions on a slip of paper or in a notes application on your computer; that way, you can just either look down and collect the information you need, or click elsewhere or the screen. Or change the names into more familiar names, like, if one of your characters' name was Jaqcueline Axaux Les-MariƩ, you can just trim it down to Jacq, and remember Jacq, Jacq, Jacq, Jacq. Remember, not all of your characters have to have full names that the readers know about. Good luck!
If you are having trouble with them a reader will too. You have to carefully watch the line between staying true to the culture and using a name that won't be confusing to the reader. I'm having the same difficulty with a story set in the middle east. You have to make sure the names are different enough that a reader can know the character by cues, like the first letters of the name or the fact that the name has a Q in it or something. Anything that runs together in your head, as the writer, is going to make some readers walk away, shaking their heads...
You could always screw the rules and go for it anyway. It depends on your setting. You could always make up something to justify it later. For example, maybe one of your French characters had a parent that really loves Japanese culture, so he or she decided to give his or her child a Japanese name.
I think that is something like balance. You can have a foreign name if it sounds nice, not only a merely copy of most used names, as I can see in literature these days. I agree with @Nilfiry, we can have a French char with Japanese name. But the better way to do this is explaining why the char has that name, or put it as a part of the plot. (in France they have a dessert called tiramysu, a lot of people thinks that it's japanese, but the name come from three french words)
I am french and I am pretty sure it's Italian, but you can find it in barely every french restaurant.
Ah, ah, ah, Larissa. See here, in Wikipedia they state: "Most accounts of the origin of tiramisu date its invention to the 1960s in the region of Veneto, Italy, at the restaurant "Le Beccherie" in Treviso, Italy." You're fancy French restaurant may have them, yet it's Italian. Huh. (I wonder why fancy Italian restaurants don't serve tiramisu?)
France, Italy.... same thing for my neurons Yes, a mistake. Why I said French? My neurons will have a little conversation with "la chacla"...