"Like Isis, River was also revealed to know The Doctor’s real name at the end of ‘Forest of the Dead,’ which is a secret so guarded that The Doctor has never revealed to any other character on the show, nor is the audience privy to this information. Indeed, by having The Doctor admit, ‘River, you know my name. You whispered my name in my ear…there’s only one way I would ever tell anyone my name; there’s only one way I ever could’ (Forest), it gives The Doctor’s symbolic power to River. Moreover, in ‘Silence in the Library,’ she is known as Professor Song and in subsequent episodes, which are all earlier in her timeline, she is known as Doctor Song. The latter equalizes her standing to The Doctor."
“Feminism, Sweetie: Denial is a River” (snippet of my research paper)