[kuschku]

That’s actually the worst thing you can do. That actually violates the relevant DIN standards for transcription.

You have to replace Ä with AE, Ö with OE, Ü with UE.

You won’t find a person named Müller under Muller in any database, especially not digital databases.

For electronic forms, always use äöüß, or, if the system happens to be an American one (the only form I’ve ever had to fill where I couldn’t use äöüß was a US DoD export declaration), use ae oe ue ss. Although be aware that some US software will have an issue with that, too, and just remove ß and assume äöü to be aou.

[tom_mellior]

Yeah, I guess you're right for German. My accents are different.

[ferongr]

Do people outside Germany even care about DIN standards?

[yorwba]

The machine-readable part of the German passport uses this DIN standard, so to avoid having to explain German orthography to some suspicious border guard, you'd better make sure you use it.

[germanier]

But when you get a US visa, the name in both the visual and machine redeable part is written with ä replaced by a, so you end up with three different spellings in your passport. And then you get a Russian visa, where they use a pretty strange transliteration into the Cyrillic alphabet (not the one I would use) and then transform that back to ASCII in the machine readable zone for variant 5. And so on.