I basically sent everything with my address on it just to be sure - even if it was written in Thai
So I guess if you have a thai bank account and a phone number you should be fine. You can get the necessary statements through their apps or ask for them in person.
And a quick update on myself. To my surprise the withdrawal request from Stars to my new thai Neteller account went through within a couple of hours. Thought I give it a try after finding out they might just ask for some screenshot of the new account, if you have never used it before with them, but that was not even necessary.
The only downside: To avoid the conversion fee I should have opened up a second currency through Netellers exchange feature before, I guess ... (I not recall being able to choose the currency when I opened the new account, so the main currency is Thai Baht)
Anyway, very happy now