Somewhere along the way someone called it: "Ping Pong," and then the U.S. board game company Parker Brothers, trademarked the name in the 1890's and put together a game kit. People were playing on all kinds of different surfaces not just tables. Since it wasn't an invention per se but just a game that people came up with, Parker Brothers didn't need to worry about any patent infringements.
They didn't have a clue how popular the game would become. In Asia and Europe, there were clubs where people would play recreationally and then major tournaments would take place during the year. Then it began exploding in the early 1900's in the U.S. but phased out for a period of time during WWI and The Great Depression, but it quickly got picked up again. In 1988, it became an Olympic sport with China being the dominant country.
Although the name Ping Pong is used a lot in the U.S., around the world and in the Olympics, it's called Table Tennis.