If you have listened to very early recordings from 1905 or so by Gauhar Jan and others, you couldn't have missed how they say, My name is Gauhar Jan etc. Looks like it was done in filmi songs (and perhaps in the theater songs) too. Here is the earliest example I could find
Listen to faulaadee-mukkaa_01_duniyaa-kee-karanee-bharanee-hai.mp3
THe singer clears says the name of the production company, the film name and the name of the character.