If 'Romanadvoratnelundar' is Romana's real name, then why do the other Gallifreyans use stage names, like the Rani, the Valeyard, the Doctor and the Master

We do not know. Numerous Time Lords and Gallifreyans are shown to use what appear to be real names (Romana, Borusa, Flavia, etc). Why certain Time Lords choose a special name (Master, Rani, Corsair, Doctor) has yet to be explained.