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I think there is some measure of the characters and their history relevant to your question. I mean, If the prince's friend knows him from childhood, and they grew up together, they would naturally...
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#2: Initial revision
I think there is some measure of the characters and their history relevant to your question. I mean, If the prince's friend knows him from childhood, and they grew up together, they would naturally have an informal way of communicating. Think about Frozen: Elsa's sister only addresses her in a formal way when she is mad at her. On the other hand, a close relationship may be romantic. They didn't grow together but the prince met the commoner girl in a tavern while he was out drinking, and got to know her better to the point where they fell in love after a few secret meetings. They will maintain a formal relationship while in the company of others (if they even happen to meet one another in a context different than a secret meeting). But they will not communicate formally in their secret meetings. My point is, don't make this choice technical. make it about the characters. put yourself in their shoes and ask: "If I was the prince/commoner and this friend I have had known me for X and we share Y, how would we be talking to each other?"