The studio behind Toy Story is named after a piece of hardware. Before Pixar made films, "Pixar" was the name of an expensive image-processing computer.
The team came out of Lucasfilm. George Lucas's company started its Graphics Group in 1979 by hiring Ed Catmull. By 1986 it had about 40 people. One of its projects was a powerful machine for processing digital images.
According to Wikipedia, a designer suggested calling it the "Picture Maker." Alvy Ray Smith, a co-founder, wanted something catchier. On his own website, Smith explains the reasoning. He grew up in New Mexico and wanted a name like "laser," a noun that looks like a Spanish verb. Spanish verbs end in -er, -ir or -ar. So he proposed "Pixer," a fake Spanish verb meaning "to make pictures."
His colleague Loren Carpenter suggested a change. Why not "Pixar"? It sounded like "radar," and "radar" sounded high-tech. The new spelling stuck, and the machine became the Pixar Image Computer.
The company name came later. When the group was spun out of Lucasfilm, it went by the placeholder "Gfx" while staff argued over a real name. Nobody could agree. With an incorporation deadline looming, Smith suggested simply using "Pixar," since the word was already linked to the group, and his colleagues reluctantly went along.
That spin-off happened on February 3, 1986. Steve Jobs paid $5 million to George Lucas for technology rights and put $5 million more into the new company. A popular belief holds that Jobs named Pixar. Smith has written specifically to deny it: the name existed before Jobs arrived.
Not every detail is settled. Author Michael Rubin reported that the name was worked out by Smith and three colleagues at a restaurant in 1981. When he interviewed them, he got four different versions of how it happened.
The computer itself was not a hit. It went on sale in July 1986 at $135,000, plus a workstation to run it, and fewer than 300 were sold. Pixar sold the hardware business to Vicom Systems in 1990 for $2 million. The name stayed with the company, which in 1995 released Toy Story, the first fully computer-animated feature film.