Rhys is the current CEO of the Atlas Corporation in the Borderlands universe. In Borderlands 3 he was introduced to us surrounded by his neon and concrete metropolis, and also donning a questionable moustache. The choice for Rhys to keep his stache seems to be canonical. With the all new announcement of New Tales From The Borderlands, we now know that he'll be returning at the very least as a cameo. Rhys' character design appears to be more or less the same, with some subtle changes here and there, his tie being the only really prominent change.

P.s moustache is easily removable if you want him shaved.