How do the deadlock ranks work?

There are eleven named ranks, low to high roughly Initiate, Seeker, Alchemist, Arcanist, Ritualist, Emissary, Archon, Oracle, Phantom, Ascendant, Eternus, and each one is split into six sub-tiers. The part that confuses people is that the badge is mostly cosmetic. Matchmaking runs off a hidden rating, so you can get put in lobbies that don't match the badge you see, and the badge itself only refreshes periodically rather than after every game. Just play a lot of matches and it settles.