"Spandex" is a generic name and not derived from the chemical name of the fiber, as are most manufactured fibers, but an anagram of the word expands. "Spandex" is the preferred name in North America; elsewhere it is referred to as "elastane".
The most famous brand name associated with spandex is Lycra, a trademark of Invista (formerly part of DuPont). Such is the prominence of the Lycra brand that it has become a genericised trademark in many parts of the world, used to describe any kind of spandex. Invista discourages such use, protecting its trademark vigorously.
Other spandex trademarks include Elaspan (also Invista's), ROICA & Dorlastan (Asahi Kasei) and Linel (Fillattice).