Mass Effect 2
After docking with the Rayya, Captain Danna greets Commander Shepard and Tali and informs them of the details regarding the charges of treason against Tali. Per the orders of Admiral Shala'Raan vas Tonbay, he does not include the fact that Tali's father is presently unaccounted for and presumed lost aboard the Alarei.
If Legion is brought aboard the Rayya, Danna is more hostile and his security detail trains weapons on Shepard's squad. He is adamant about denying Legion entry, citing that neither geth nor Cerberus is welcome in the Flotilla. Shepard can convince him into letting Legion aboard, or comply with his demands and leave Legion aboard the Normandy.
Danna refers to Shepard as Captain, despite the Commander not being part of the Alliance military anymore. His reasoning is that every commanding officer's decision on their own ship carries great weight.
Mass Effect 3
If the quarians lose their war with the geth over the skies of Rannoch, the entire fleet is destroyed, along with the Rayya. The ship's final moments are heard in the form of distress calls from Captain Danna, who reports that the ship is falling from orbit and the drive core and escape pods are inoperative.