How did they come up with the name “Pixar”?
Pixar originally was the name of a computer that was developed by the Computer Department of LucasFilm for digital compositing - Pixar Imaging Computer.
Taken from To Infinity and Beyond on naming the new computer : Alvy Ray Smith grew up in New Mexico where Spanish was the second language, and the infinitive form of the verb always ends in ‘er’,‘ir’, or ‘ar’. He "suggested ‘Pixer’ an invented Spanish verb that means ‘to make pictures.’ Loren Carpenter said, “Well, radar ends in ‘ar’, and it’s got a kind of high-tech feel to it. Why don’t we use ‘ar’ instead of ‘er’?” And that is where 'Pixar came from.
Woah, that is really cool!
I always thought the name was a portmanteau of ‘Pixel’ and ‘Art,’ but I don’t have any evidence for that claim so I might have just made it up, Hannahmation is probably correct.
I always asked myself about this 
I also thoght it was derivated from “pixel”.
Intersting thread and responses to PIXAR name origin.
I would have thought that PIXAR was somwhat of an
acronym for (and, my own creation/guess here):
PIXel Animation Rendering = PIX A R or (concatonated) PIXAR.
Easy! One day, God brought down the “Holy Three”. Now, these “Holy Three” had a commandment to accomplish by God. These “Holy Three” had to take the pictures and make it into moving art! Impossible! One of the “Holy Three” asked God, “What are we going to name this?” and God replied, “Art challenges the Technology”. The “Holy Three” had no clue what this meant, so they decided to call it, “Moving Pictures of Art”. This went on for a year or so. But, one day, I lightning bolt came striking down and destroyed the company sign. The only letters that were standing were P - I - X - A - R.
There you go! That’s how they got it!