The finger next to your little finger is known as the ring finger. This is the finger which custom dictates that you wear your ring. If you are married or engaged custom dictates that you wear your wedding and/or engagement ring on the ring finger of your left hand.
Normally those who have a military ring, or class ring will wear that ring on the ring finger of the right hand. The trend that I have seen in recent years is that people will wear their wedding ring on the ring finger but they will wear the military ring on a different finger of either hand. I have even fitted military rings for customers to wear on their thumbs.
If you want to use some wisdom and avoid any possible problems wear your military ring on the ring finger of your right hand while in formation. It might be a good idea to wear it the same way whenever you are in uniform but their is no rule or regulation that I am aware of which says that you have to.
You won’t be wrong whichever way that you decide to wear your custom military ring so my advice to you is to wear it on the finger where it feels most comfortable. If you want people to really notice your new military ring do something wild and wear it on your thumb.