In short, yes. A bit longer a story:
on the web in the US
Actually there is no such thing. Worldwide is the name of the game.
names like Amélie, Jôse, 王
Accents and such ARE important. People from France or Spain or Korea would have their own computer support for these special characters as a matter of course. They usually keep them when moving, for example, to the States. Your name is precious. Not all folks will adapt for easy acceptance while integrating in the new environment.
car insurance quotes
Best verify what the people in Quotes accept. There should be some guidelines. And in Invoices :-) Generic banking requirements may help here. Non-alphabetic character sets like 王 may be out for procedural reasons.
and we also pass on the data
Also better check out what the receiving parties support. There SHOULD be something written down as it is beyond company borders. Or you can scrutinize what you, in turn, receive from them. Last resort, that.
The technical side: Best keep names separate from the OS. So avoid filenames. Check/test database support settings.