This was suppose to be an edit to my above post but I took too long.
"Please correct me if I am wrong, I think you said the original photo stays Photos, where the photo with the names remains in Notes."
I believe you are correct. I'll quick double check to make sure.
Edit.
The double check on my iPad 4 using IOS 10.0.2 shows the original photo remains in Photos and the captioned photo remains in Notes. The whole reason I ended up confusing you with the crop was in case you wanted to add the captioned photo back to Photos. You could take a screenshot in Notes then crop the side bar.
I also noticed if you move a photo to Notes you can caption it in Notes, you don't need to use the pop up window if that's not handy.