I really don’t get the “say my name” thing, it cringes me a bit ╮(￣▽￣)╭

Maybe... just maybe, it was inspired by japanese BL's, since it's a common scenario in yaoi, and they call people by their last names unless they're really close friends, or intimately close (▰˘◡˘▰) like lovers, that's when they switch to calling each other by their first names.
This is just a thought. There could be other reasons though. (●'◡'●)ﾉ