The government being this sloppy at getting accents right is surprising, I would expect them to value accuracy and a clean paper trail when handling names.
Ü isn't even a special character or utf-8 - ü is part of ascii. How does this even fail? Is their database a 7-bit database?
But I wouldn’t bother memorising that and every other possible way that the other person has to press the keys depending on their keyboard layout and operating system. I’d just tell people to put u instead.