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

There is no regulation on this. But part of tradition is for Officers to address junior Officers by first name. This is also the reason that Artillery units have a nickname for just about every rank and/or position.

No regulation I know if. I had someone that used to do it. His explanation was it build a repore in the office and makes it seem that the higher ranks see you as a person not just a warm body

It's called a norm.

There are none. This has become a common practice particularly for senior officers. It never bothered me, or anyone I knew. It was awkward at first, what is the harm. Also, they did not address people that way in open environments. Thank you for your service.

It is called, Leadership's Discretion.

It is a custom, when the higher ranking officer likes / respects the lower ranking officer.

My AIT was at Lowery AF Base in Denver. My father, a retired Maj, was attending my Graduation. He saw the name of my Commander of the Army Detachment Unit. He wanted to see the commander’s photo. As we were walking towards the office, the commander walks out of his office, and my father calls, “Hey Tom!” This E-4 was trying to find a hole, as the Commander is turning around to see who dare call him by his first name. Sure enough, the Detachment Commander had worked for my Dad.

No reg. But it was not unusual. But mostly in private or semi private settings, staff meetings, between general and aid, etc. As a captain on staff 1CAV I was more than once referred to by my first name by the Div CDR and thought it was no big deal and I understood it was not an invitation to become his BFF.

Something funny, related to the question though. I spoke to a veteran who told me that when he was in he was usually called by his rank and first name. It seems people weren't comfortable calling him by his last name, except one female LT. Sweetheart was his last name.

As a 1SG in an aviation company, it was ALWAYS MAJ Whatever and First Sergeant Beal in public. ALWAYS. In front of officers or enlisted folks. ALWAYS. Behind closed doors, it was first names. We both respected the institution and each other.