Apparently it didn't apply to my bank when I tried to change my name with them, according to them anyone could have made my change of name form, and having ID and correctly putting in the PIN for my card wasn't enough

The Belgian DPA had at least one bank pay a fine for their incompetence: https://gdprhub.eu/index.php?title=APD/GBA_(Belgium)_-_141/2...

Depending on how strongly you feel about this, there's a good chance you'll win if you take your bank to court.