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

Google

I was aid to a one star and in private he would call me by my first name but otherwise he would call me Sgt. He was a solders General and I would have gone across hot coals for him.

In private OK. Otherwise NO.

As i said in my first reply, this was never a concern for me. I always thought it unprofessional, but.... However, there was one time that this first name business bothered me. Not just the first name issue, but there were other issues I had with the command in that unit. I was assigned to an Apache unit and we deployed to Germany for Reforger. The Apache was new and ours was the first unit to get it. It was important that the NATO partners see the Apache as a success. Every mission flown was watched by foreign country observers. A mission with 12 AH-64's was supposed to launch at midnight and be over target around 0115. The weather was terrible, fog and low ceilings. the weather detachment said the target would probably be clear at the time the mission was to be on target. The BDE CO was talking with the BN CO who did not want to fly the mission due to weather. The BDE CO said, "(Insert first name), we need to fly this mission." So, the mission launched as scheduled and one aircraft flew into the side of a hill. As I said, I had other concerns about our leadership. But I thought for the BDE CO to have that conversation within hearing of the enlisted soldiers in the TOC was not a good idea. Several months later I moved on and I heard through the grapevine that the Brigade was selected to deploy on Desert Shield, but could not. It seem they were lying on the USR and a lot of things were not combat ready. Granted I heard this through the rumor mill, but I can believe it due to the things I saw first hand for 2 years.

In the Chief's Mess we address each with familiar names. In front of Sailors/Troops it is always Chief, Senior or Master Chief. It is good for order and discipline to maintain proper bearing. You never know what order must be given.

Brandon,
I looked all over the place trying to find a section specifically allowing the use of first names. I did find information that specifically addresses Senior/subordinate contact.

In the Air Force of the 60s the line used was: Rank amongst company grade officers was like virtue amongst whores.

It is probably in the Common Sense Regulations that would cover all situations that may arise in any branch!

Honestly, I hated this. I didn't want to be friends with my boss; I'd rather have a mentor over a friend in my bosses.

Article 134, the "just because" article.