I've found a few lonely bottlecaps out on the wastelands, but I was wondering if you can get them out of your inventory onto a table to make, say, a bottlecap pyramid. As a bonus question I was also wondering if you could give your companions bottlecaps since I believe their efforts should be rewarded.
You cannot physically drop your own personal caps. This is due to the fact that they are no longer an item in your inventory like they were in Fallout 3.
The only way I have found place a single cap somewhere was to explode a bottlecap mine, which spawns roughly 30 caps, and proceed to drag them elsewhere. This only worked for me because I didn't need very many caps. I was only making a Nuka cola display in my house. If you need more than this you'll need both a lot of bottlecap mines and a lot of time and patience. This is the only way I have found so far hope this helps.
PS. if you just so happen to accidentally pick up one of the caps while moving them you take them all including the ones you placed so try to save often when moving them otherwise prepared to be triggered.
There's one way to store your caps but not in a pile. Simply build shops and they will be stored in the shop. If you want your caps back, scrap the shop and the caps will appear in your workshop inventory.