Also it is discrimination because it's a different name and the difference can lead to issues which can cause non small monetary harm.
But technically your point about transliteration is a valid solution (and one that I have actually seen in practice in banking systems) - the bank is free to transliterate the name to something that fits in ECBDIC, as long as it also then appropriately transliterates it back to use the proper name in the documents and communication. The law doesn't mandate any technical nuances of data storage, as long as they get the proper result.
Do you have a source for that?
There are official state languages, which have official alphabets, which include non-English letters. There are legal names of people and organizations which include non-English letters.
The law requires the bank to have and apply correct customer information, and spelling someone's official name wrong is simply not acceptable.