I believe the term is related to regulation 20 in the Canada Labour Code regulations, and that provides that the competent person has to be approved by all parties, so that by definition, if it's going to be a competent person, the complainant and the employer should approve the individual as such.
I don't practice in this domain—I don't practice at all, I'm just an academic—but what I've heard is that it works pretty well for the physical violence right now, which is the primary purview of that regulation. The person who is named has to be agreed upon by the target, by the employer who is supervising, and by the union, I would think, because if you have a health and safety committee, then that's part of that.