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

It would be done in privacy only. Otherwise rank and last name only. Never seen it done myself. I have been called son a few times when things got hairy.

I didn't have any issue with it. I was even allowed to call some seniors by their first names. Outside of work.

However I had an issue one. A CPT called me Tyrone and when I informed him that was not my name, he said whatever. I politely informed him, that if he wasn't aware of the correct saying of my name or deliberately choose not to say it correctly, he could address me by my rank and last name. Again, he blew me off so I walked off.

A fellow NCO told him I had just been apprehended for bringing a firearm on post. He was very polite after that.

For a higher ranking officer or NCO to call a lower ranking person by their first name indicates a personal connection or a level of trust. My commander who called me by my first name for years honored me. He was an honorable and strong leader and he didn't call everyone by their first name. So as far as a regulation, well there is no REGULATION on personal connections or a level of trust between military personnel, nor does there need to be. It is all about trust and respect. Not about regulation.

I don't believe that there's any regulation dictating what you call your subordinates by any names. I think in common courtesy and professionalism that is used as guidelines.

What's the regulation for calling you by your last name?

I’ve been for quite a while, but some of my NCOs and officers would call me by my first name or shortened my last name.
I was never bothered by it.

There is no regulation. It is held in tradition. In most cases, if an officer of senior rank addresses a lower ranking officer by his/her first name, then it is usually because the senior officer has high regard, admiration and trust in the lower ranking officer - and the lower ranking officer usually has high regard, respect, trust, and loyalty for the senior ranking officer. This is normally forged in a working relationship where both Officers have risen above trials and tribulations through training exercises and real-world missions together where they have formed a trusted and cohesive bond. Usually, if a senior ranking officer addresses a junior ranking officer by their rank instead of their first name, it is normally because they have not worked together or have had very limited exposure to one another and have not formed a trusting bond. To be called by my first name by Colonels, Generals and by a few Admirals meant I was trusted by these senior officers. Those who addressed me only by my rank usually didn't know me or they were the few who didn't like me... and those few had problems anyway for which they were later investigated and one was court martialed. Therefore, take being called by your first name as a sign of trust and respect. Watch the TV show - The Unit... notice how the Colonel always addresses his team.

For me it was always based on the individual I was dealing with.

Something like this would fall under Military Customs and Courtesy.

I always used the officer's first name in talking to him unless there was a good reason (discipline etc) not to. Calling a subordinate by his rank immediately becomes a bar to open dialogue and emphasizes the hierarchical structure which is counter-productive.