The most famous falling-block game is half named after a racket sport. Tetris is "tetra" plus "tennis," and the tennis has nothing to do with the gameplay.
The game came from Alexey Pajitnov, a speech-recognition researcher at the Dorodnitsyn Computing Center of the Soviet Academy of Sciences in Moscow. He wrote it in Pascal on an Elektronika 60, a Soviet computer. Wikipedia notes that sources disagree on the date. Some give June 1984, while a BBC documentary suggests spring 1985. Britannica says 1985.
The idea started with a physical toy. Pajitnov bought a pentomino puzzle set, the kind where you fit shapes made of five squares into a box. Pentominoes come in twelve shapes. He scaled the idea down to shapes of four squares, called tetrominoes. Counting mirror images as different, there are only seven. Those seven shapes became the Tetris pieces.
That count of four gave him the first half of the name. Tetra- is the Greek combining form for "four," the same element as in tetracycline. Britannica says he took it from the four squares in each block. The second half, according to both Wikipedia and Britannica, came from tennis. Wikipedia calls it Pajitnov's favorite sport. The result sounds vaguely scientific and vaguely playful, which suited a game built by a computer scientist at a research institute.
The name then had to travel through a tangle of Cold War licensing. Robert Stein of Andromeda Software found the game in Hungary and approached the Moscow computing center for rights. He sublicensed it to Western publishers, including Spectrum HoloByte. Elorg, a Soviet state organization, eventually took control of licensing. In 1989 Nintendo secured the rights for the Game Boy and the NES. Britannica credits the Game Boy with making the game a star.
In 1996 The Tetris Company was formed to manage the name and rights, as a partnership between Elorg and Blue Planet Software. By then "Tetris" had become a brand as well as a game.
The name has outlived its own explanation. Plenty of players know every piece by shape without ever noticing the tennis hidden in the title.