Anyone know what Army Regulation (or any branch) that allows a higher-ranking officer to call a lower-ranking officers by their first name?

Not sure about the Army, but for most of my 20 years in the Navy, I didn’t people HAD first names-LOL. Seriously though, about the only time I would use a guy’s name was on his annual evaluation. When I made E-7, I was assigned a “first name”, which was “Chief”, and that’s how my guys addressed me for the last ten years I was in. It’s been 30 years since I retired, and that first name has stuck. I love driving on to almost any military base with a civilian guest, the gate guard handing back my ID and saying “Have a nice day Chief”. When my guest asks “Why did he say that, does he know you?”, I always answer “No, but he knew my first name”.

lol..there isn't one

Calling a lower ranking officer by their first name was very common practice in my units. No one ever thought twice about it.

I can't think of a single time I was addressed by my first name and had it be a bad thing. Getting a decent FITREP, goodbye handshake from the CO at his hail & bail, a DH encouraging me to push harder during a PRT (and subsequently getting my best score at that command) or even just a "thanks" from my DH for getting something extra done being what he needed from me that day.

Aside from taking the watch, though, rank was not something you wanted a senior Officer to refer to you by. Billet. Mr Last name. First name in the wardroom. All good. "ENS Schmuckatelli" is probably not going to like the remainder of that conversation, though.

This is something that's been around since I joined the Army in 1979. Company level commanders (CPTs) calling their XO's or PLT leaders (LTs) by their first names was common. Bn CDR (O-5) calling their XO (MAJ) his/her XO first name also very common. Why is this an issue?

You can call me whatever you want, just don't call me late for a meal.

Military respect is paramount. Undo familiarity can lead to a breakdown in morale and is bad leadership. Eval and Fitrep time will suffer from this kind of behavior and one day you will have to issue an order which will become an issue do to Likership.

I don't know of a regulation, however, it is bad leadership and could lead to mistrust by junior personnel. Military respect is better than the perception of undo familiarity. Break down in morale especially with evals and fitreps.

It’s not so much being allowed as it is not being prohibited.

I only did that once, in a specific situation; it was kind of an instinctive response to a vet who was having a flashback and thought he was in combat in Vietnam again; a place where a woman calling his given name sternly, and telling him to stop it, would be unlikely to happen. Thankfully, it worked and he stopped tossing my corpsmen around like rag dolls. Had I taken time to stop and think, I might not have done that; but my guys were being hurt and he, being our patient, was not someone to do harm to even in self defense. By the time we called in a doctor to order a sedative, who knows what might have happened? Frankly, I know of no such regulation, and too much familiarity does tend to breed contempt, as the old saying goes. There are other ways to gain respect and cooperation generally.