We actually do it the other way around in roses and irises: We enter the regular Latin letters in the main cultivar field and enter the names with diacritical marks in the also-sold-as field. Otherwise, the names don't end up in alphabetical order because the system doesn't recognize the names with diacritical marks and puts them ahead of all the other plants beginning with that vowel or consonant. This results in duplicate entries because the name of the plant is not found in the logical place in the list of plants in alphabetical order.
As for umlauts, I think the conventional transliteration practice is to add an "e" after the regular Latin character. Dornröschen therefore would be transliterated Dornroeschen.
