Technically, the first was Lobachevski (published in 1829-30). Bolyai was independent (published in 1832). Gauss discovered it independently of both (not published).
A more complicated research is needed to find out when it was actually discovered by each person, and we can never be 100% sure of the result. Perhaps Gauss was the first. But the usual way to establish priority is the date of publication.
All three discovered ONE non-EucludieanEuclidean geometry (hyperbolic geometry). Riemann's contribution was a more general approach, introducing infinitely many possible geometries (Riemannian geometry).