Usually they'll accept it, but some parts of the backend are still running code from the 60's.
So you get your name rendered properly on the web interface, and most core features, but one day you're wandering off from the beaten path, by, like, requesting some insurance contract, and you'll see your name at the top with some characters mangled, depending on what your name's like. Mine is just accented latin characters so it usually drops the accents ; not sure how it would work if your name was in an entirely different alphabet
Guess what, I'm part of this 70% and I also work in a bank and I know exactly how.
Not a single letter in my name (any of them) can be represented with ASCII. When it is represented in UTF-8, most of the people who have to see it can't read it anyway.
So my identity document issued by the country which doesn't use Latin alphabet includes ASCII-representation of my name in addition to canonical form in Ukrainian Cyrillic. That ASCII-rendering is happily accepted by all kinds of systems that only speak ASCII.
People still can't pronounce it and it got misspelled like yesterday when dictated over the phone.
Now regarding the accents, it's illegal to not support them per GDPR (as per case law, discussed here few years ago).
Why can't these people understand that that 70% of the world consider ASCII to be "the computer language", not English, and UTF-8 to be "whatever soup that only works inside files and forms and can't be program manipulated"?
Maybe it needs to be communicated more often, like way more often, until it sticks.
For some reason they have a hard-on for putting last names in capital letters and they still have systems in place that use ASCII