I read the Dada manifesto on YouTube. It was fun. One detail that's amusing. It makes the point that Dada means nothing and the name doesn't need an origin. But Tristan Tzara engineered his own name to mean painful melancholy or painful pain. Probably.
A lot of writers and artists, especially in the 20th century played word games like this. Language jumping to get redundant or amusing names nobody would ever figure out. I guess it could be a coincidence, but damn that would be a funny one.