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

A traditional gesture of respect and fondness, nothing more, like the others have said here. I did it as well and it let my subs know they meant something to me in leadership.

To me being addressed by my senior NCO(s) and officer using my first name meant they had trust in me to ensure during exercises I would provide the right information to execute the actions needed. During deployments the right mix of equipment and personnel would reach the destinations in the stages as needed. The only time I recall addressing an officer by his first name was in Vietnam. LTC Frank Fish worked in the ALCE and we played basketball together while off duty. He insisted I call him Frank on the basketball court.

True. My squad had it's own chemistry that seemed lost on everyone BUT our senior leadership: we were all on a first name business in the workplace. The mindset is, we are a family. Last names and ranks are for business, first names (which we jokingly called our "free" names,) are for all other matters.

When I worked for the division Provost Marshal with the 8th ID In Germany back in the early 80’s. We had a first name relationship. He called me “Don” and I called him “Col . “

Thank You SSG Hartnett "AR 600-20" Without friendly interactions it would limit the ability to confront the problems encountered by command roles- RESPECT IS THE WORD

It seems that is the custom in the British SAS...

Don't know of a regulation, but I had a colonel that told me we would be on a first name basis. He would call me Don, and I would call him colonel.

The non-existent one.

This is a "lighten up" Francis-type of post. It was okay for a GO, or Group commander or other superior to address me informally by my first name.

It was common when i served