"Müller" and "Mueller" are actually different names. But if umlauts aren't available, "Müller" should still be represented as "Mueller", "Muller" would be just

"Müller" and "Mueller" are actually different names. But if umlauts aren't available, "Müller" should still be represented as "Mueller", "Muller" would be just wrong. Ordering also depends on the context. Usually "ä" is sorted like "a", but in lists of names it's sorted like "ae".