I can speak up as someone with some experience and success on this count.
At present I am married to my best friend of nearly 25 years (married nearly 15), so well aligned, and a bit over a year ago we added a friend of ten years who approached us both in a way that surprised us all but that has turned out to be an extraordinary gift.
We don't call ourselves a triad, a triune, a trireme, a tricycle, a triskelion, a tripod, or a tri-anything-else. We're just us. And interestingly, it seems to me that our more politically and religiously conservative friends embrace and support us as a tri-unit all the more, without requiring a label nor laying any on us. It's our more liberal friends who try to slam such things into categories and then gossip about them viciously. Which is why we have avoided being out in the liberal organization where we all work: we've seen the gossip applied to others in "poly" situations.
I'm of the view that Michel Foucault espoused in the 1970s and 1980s. It is one thing to do certain acts as inclined. That can be liberating, particularly when they transgress assumedly fixed social orders, and in transgressing them, expand them in good ways. It's yet another when those acts are jammed into categories. That simply reifies the social order's power to define each and every one of us as a category, based on certain behaviors, then police those categories and behaviors.
As soon as those categories and labels come up, people spend more time bickering and dramatizing and intellectualizing over them than simply living their lives with integrity and dignity. I have never had time or energy for that. Like calypsoblu notes, our three-person unit has been entirely lacking in drama. Yes, we have our issues with each other. But that's because we are people, not because we are three people.
It was rough at the beginning for certain reasons involving our all having long-standing habits challenged by our own hearts. It was scary because it was new and unexpected. But all in all, the levels of comfort, support, respect, warmth, and fun have been increasingly, amazingly sweet. I'd rather it be called "successful relating" than any category that focuses on number and implicitly suggests that we aren't normal because of a number.
We aren't normal, by the way, but not because we are three. We are not normal because we have successful, calm, productive, mature, mutually supportive, deeply caring, interrelating devoid of drama and gaming.