Ah, what to call each other. What a conundrum for many of us. I well remember how difficult it was for me to change from saying "Dr. Sturz" to addressing him simply as "Harry." Linguists call this "language pragmatics." People of the same relative status might use any number of expressions depending on how intimate they are with each other. Terms of address give us some idea of just how complex it can be to match forms and context. Transitions in naming can be particularly difficult. They usually involve changing not just a habit but a whole set of social assumptions that go along with naming. An example might be the uncle who tells his nephew, "You're much too old to call me Uncle Bob anymore. Just make it Bob." Notice two things here:
1) An unequal relationship based on a generational hierarchy is being replaced with a peer relationship based on mutual adulthood.
2) It is the hierarchical relationship that entitles the uncle to ask the nephew to make the change. The nephew would have had to ask permission first.
(NOTE: This is just an example. I personally prefer to be called "Uncle Dave.")
Now why am I telling you all this? Between peers, a shift from title plus last name (Dr. Sturz) to first name (Harry) not only serves as an invitation to redefine a colleagueship as a friendship, but it also has important ramifications for communication in terms of what topics may be raised for conversation between parties or what personal information they may wish to share. I have seen this happen with several of my former doctoral students who became professors in various institutions. I invited the switch from "Dr. Black" to "Dave" because the latter better reflected the new reality that we were both now peers in the academic world. I don't imagine this shift came easily for them. Some took to it like fish to water. Others felt they were not yet were ready to make that switch. I am fine with that, though I hope their hesitancy is not due to anything on my part.
Knowing how to relate surface forms with particular communicative goals is a central goal of linguistic studies. I remember being a Jesus Freak in my teens and frequently referring to Jesus as my friend. Of course, he was (and is) just that. Jesus told his disciples as much ("I no longer call you ...."). But here's something I noticed when I began reading the Gospels. Not once did Jesus' closest disciples address him as "Jesus." It was always "Lord" or "Master." There was, I suppose we could say, always a respectful distance between intimate companions.
In the end, I think we need to give people a lot of latitude as to how they should address us. But I for one have no problem with a former student making the transition to "Dave."