The synthetic fiber spandex was discovered by DuPont chemist Joseph C. Shivers. The original material was called Fiber K, and later DuPont labeled the name Lycra to distinguish their particular blend.
However, the general product has long been called the spandex. The fabric got its name just because of what it does. Spandex is an anagram, a mixture of the letters of a word to create a new word, from the word "expands".
Interestingly, the term "spandex" is only captured in the country for its invention: North America. Elsewhere in the world, the fiber is usually referred to as "elastane" (or variants thereof), which still refers to the extreme elasticity of the material.