Is it possible to lose Onyx rank in Halo 5? Or, once you are in Onyx, do you just stay there and your number (onyx-specific rank) changes?
As of right now, no. Once you reach Onyx, you will stay at Onyx. You will be able to see your pure CSR, which starts at 1500. If you lose matches while at Onyx, you will just go down to 1500. While at lower ranks, you can move between the rank (bronze, silver, gold, platnium, or diamond) you are in (from 1 to 6), but you cannot lose a full rank.
Example: You cannot go from Onyx 1500 to Diamond 6 or Gold 1 to Silver 6, etc., but you can go from Gold 2 to Gold 1.
Eventually, there will be seasons that will reset your ranks at the beginning of each season.