The Mesa project was originally started by Brian Paul. Here's a short history of the project.

August, 1993: I begin working on Mesa in my spare time. The project has no name at that point. I was simply interested in writing a simple 3D graphics library that used the then-new OpenGL API. I was partially inspired by the VOGL library which emulated a subset of IRIS GL. I had been programming with IRIS GL since 1991.

November 1994: I contact SGI to ask permission to distribute my OpenGL-like graphics library on the internet. SGI was generally receptive to the idea and after negotiations with SGI's legal department, I get permission to release it.

February 1995: Mesa 1.0 is released on the internet. I expected that a few people would be interested in it, but not thousands. I was soon receiving patches, new features and thank-you notes on a daily basis.

That encouraged me to continue working on Mesa. The name Mesa just popped into my head one day. SGI had asked me not to use the terms "Open" or "GL" in the project name and I didn't want to make up a new acronym. Later, I heard of the Mesa programming language and the Mesa spreadsheet for NeXTStep.   More detail...