I’ve never really cared about students having English names or not, as long as they can spell their names consistently.
When I had an employer who insisted every student needed an English name, one day a new student proudly proclaimed he didn’t have one “因為我很愛國”. He wasn’t arrogant about it, just proud. He had obviously been coached. (This was over in 大陸land.) I would have accepted that, but an assistant (Chinese) teacher said we couldn’t accept it and proceeded to talk him into choosing an English name. It took about two minutes, and after that everything was fine. 