One big issue that users of non-roman alphabets have is phonetic names. The way Google handles things, and I think their approach works very well, is via two custom entries,
X-PHONETIC-LAST-NAME. If DAVdroid could sync these fields, that would be ideal.
Without phonetic name support, DAVdroid is … well … not very useful for people in Japan, China, or anywhere else where the standard alphabet is actually a character set (and not really an alphabet) with thousands of characters.