Uh I see. I didn’t know any of those people, so I had to google that discussion between Alex O’Connor and Wiliam Lane Craig. Listened along for quite a bit and it was actually very interesting (so thank you, I’ll definitely finish listening to the whole thing later on).
From the way the used that “technique” I am guessing it isn’t really that much about Christianity but rather, as others have said, a way to connect to the other person. People often get understandably heated during theological debates (understandably so, our most important beliefs are being challenged), maybe calling the other person by their name is a way to try and remembering the human and forming a sort of emotive connection that could otherwise get lost during the discussion.
Why specifically Christians? I don’t have an answer to that one. I am guessing it might happen more frequently with religion talks rather than say politics, or other frequent topics of discussion, because religion tends to appeal more often to morality and thus emotions. Just a guess, though.