Of course English used to have formal and informal pronouns: "thou" was informal and "you" was formal. But over time it came to be considered polite to use the formal in more and more contexts until the informal was lost.
In religious circles people sometimes use "thou" to refer to God because that's how he's addressed in the King James Bible. I once heard someone say that we should address God as "thou" to be more respectful, which is a little amusing because it's exactly the opposite of the intent of the King James translators. (Off the top of my head I don't know if the thou/you usage in King James reflects the Greek and Hebrew or if that was something interjected by the translators.)
Today we generally indicate formal address by using a salutation and last name, and informal by using a first name. Like "Mr Jones" versus "Bob". And of course there are all sorts of things we do differently in formal versus informal speech, like in formal speech we avoid use of contractions and slang terms.
Your example reminds me of another Poul Anderson story, I think it was called "Day of Burning", but anyway, the story where humans have their second contact with the Merseians. Anderson says that the humans learned the Merseian language on their first visit, but by the time of this second visit the language had changed a great deal creating difficulties in communication. And so when he wants to show that the humans are speaking in an out-dated version of the language, he has them use Shakespear/King James type speech, saying "whither thou goest" and that sort of thing. I think that effectively gives the idea of how they would have sounded to the natives.
Likewise, if I was writing a novel and wanted to convey to the reader the idea that the level of familiarity between two people had changed to the point where they were now using informal speech, I think I'd have them saying, "How do you do, Mr Jones" at the beginning and "Hi, Bob, what's up?" later. The reference to shifting to the informal pronoun works for me because I know what he's talking about, but I'm sure many readers would not understand. Well, Anderson tends to write for a more literate audience, perhaps he was counting on most of his readers understanding.