If you read Star Wars screenplay, you will notice that neither C-3PO, nor Ben Kenobi, nor Leia in her holomessage ever refer to her as a "Princess" (or even mention her name, for that matter).
Moreover, Luke didn't know who she was as public personality:
LUKE: Who is she? She's beautiful.
THREEPIO: I'm afraid I'm not quite sure, sir.
LEIA: Help me, Obi-Wan Kenobi...
THREEPIO: I think she was a passenger on our last voyage. A person of some importance, sir -- I believe. Our captain was attached to...
and the message itself:
LEIA: General Kenobi, years ago you served my father in the Clone Wars. Now he begs you to help him in his struggle against the Empire. I regret that I am unable to present my father's request to you in person, but my ship has fallen under attack and I'm afraid my mission to bring you to Alderaan has failed. I have placed information vital to the survival of the Rebellion into the memory systems of this R2 unit. My father will know how to retrieve it. You must see this droid safely delivered to him on Alderaan. This is our most desperate hour. Help me, Obi-Wan Kenobi, you're my only hope.
As a matter of fact, the only times the words "Princess" or "Leia" appear in the script when breaching the 4th wall (e.g. scenario referring to her, NOT as part of character speech)
Yet, Luke seems to know right away that she's a Princess on board the Death Star:
THREEPIO: Princess Leia.
LUKE: The princess? She's here?
HAN: Princess? What's going on?
Is there canon explanation (perhaps from novelization) of how he knew right away that his "lovely" girl (quoting from screenplay) was the "Princess Leia" that C-3PO was referring to?