Rao could be a surname or a last name in Andhra and Telangana...When I say last name, it is just like title or can say middle name.. Rao having at the end of the name need not be for brahmins alone.. Kshatriya's also do have... Infact any caste can have it.. Rao having as a surname i am not sure of caste.. i give a famous telugu movie actor name.. his name is "Rao Gopal Rao"... lol... Where First Rao is the surname and last Rao is generally followed with main name like take it as middle name..many movie actors do have it like NT rama rao, Akkineni Nageswara Rao etc., Or KCR (Telangana CM) or PV Narasimha rao (ex PM)... Old generation people used to have it... When take Reddy, it's actually caste name..
Few names that people generally add to their names irrespective of caste are Rao, Murthy, etc.,