When speaking Latin .... do as the Romans do, is one method, and I use it.
In Japan I always use (surname)(given-name) order when writing in Katakana, or when pronouncing my name in Katakana while speaking Japanese. If talking to a person in English, then I will use English pronunciation and (given-name)(surname) order. If, in Japanese, I am asked to pronounce my name in English, then I will use (given-name)(surname) order to do so. My meishi has English on one side, Japanese katakana on the other, and the different order on each.
It has worked out fine. Occasionally someone newly met person will request confirmation, but I think that would happen no matter which system was chosen due to the inherent ambiguity.
Japanese people overseas seem to use the same system, matching their name order to the language they are speaking.
I don't think there is a general fixed rule, but there may be a rule in your company or school.