All I can imagine is Morpheus crankily walking around wrapped up in a blanket really. ENJOY THAT IMAGE WILL YOU.
Consider it done and expect him to be condescending as fuck.
Maybe they were initially like, professional with one another AT FIRST AT LEAST. Because Morpheus' studies might center around politics a lot, and Merlin may lol at all the people Morpheus will offended but he'll be calling Merlin a bonehead from time to time too, not gonna lie. He'll also rant. A lot.