Wild elephants may have names that other elephants use to call them
npr.org
npr.org
Source?
I suspect the quiet part of the three assertions is "under human supervision".
You can certainly visit various zoos and purchase art by elephants and watch them paint with brushes on large canvases.
Typically less dense than a Jackson Pollack and less use of spaghetti than a Pro Hart* carpet.
Is not clear to me if they just parrot the training or really try to send a message or draw some scene that they find instinctively pleasant. (but wouldn't be strange having in mind their intelligence).
The other animals have nicknamed the elephant "Two Tails", and it explains that it is afraid in battle because it can think about what happens when a shell bursts, and ruminates upon whether it might not be better off back at home in the forest rather than here in the army...
Another study already showed that some monkeys have vocal words to designate a tiger and an eagle and use that to make all the group go up or down in the tree depending where the threat comes from. Elephants being more complex animals also living in groups are quite likely to have an even more elaborated language.