Who is the designated person, and can a coach be one?

Every sport organization must identify one or more designated persons with specific responsibilities under its removal-from-sport and return-to-sport protocols, and those responsibilities can be shared between individuals. Ontario's page says coaches may take on the role of a designated person; it does not list the responsibilities there (they are in the protocols, covered in the other answers).

Sources: https://www.ontario.ca/page/rowans-law-concussion-safety and https://files.ontario.ca/mhstci-rowans-law-protocols-en-2020-05-13.pdf