There is a concept of a pro account. For example Professional accounts and games on OGS
I think certain special tags/colours were made for example for the American E-Go congress when it was played to highlight the advisors/organisers red/orange name and a tag/image to say AGA staff.
I don’t see why in principle this couldn’t be extended to teachers, but I guess one would have to define who should qualify for such status, and if they are professionals, then there is already the professional colour/tag etc.