I tried to set my display name to:
نصر الدين تهريب الحمير
That is composed entirely of letters and spaces, Unicode-wise.
Yet the profile editor rejected it on the grounds that it wasn't composed of letter and numbers and/or didn't start with a letter or number.
So, either the message needs to say, 'starts with a number or a latin alphabet letter', or the checker needs to changed.
Note that this question has nothing to do with whether non-Latin names are permitted. It was easy to stick a zero on the front and use it.
The Bidi bugs that this is exposing are a bit of an extra bonus.
edit
Full disclosure. This is not my name. I'm not complaining about freedom of expression. If the site changes to reject نصر الدين تهريب الحمير, I have no cause for complaint. However, accepting <0 نصر الدين تهريب الحمير> and rejecting without the zero seems a bit odd, and the error message is, I claim, certainly inaccurate.
Google translate will tell you everything you need to know about this string. It goes with my new gravatar.
The Chinese string should be self-evident when Google-translated. For the Arabic, if you need help, post a question and I'll be happy to type in all the details in an answer.
NOTE
This idea of RTL display names seems to have been in the water: see this.
I don't think that this should be closed as a dup of that, since I'm noting the problem with the profile form validation, not the display problems that ensue.