Actually the group's founder, Peter Green, had to coax McVie into joining the band (after Mick Fleetwood had already committed to leaving Mayall) by naming the band, "Fleetwood Mac".
http://www.youtube.com/watch?v=O8RhZDGLEXM
I went to a concert to see Long John Baldry, who was a no show. Two other bands were there that I didn't know at the time; Fleetwood Mac and Savoy Brown. I wasn't disappointed in either. As you likely know, there's Fleetwood Mac with Peter Green, and Fleetwood Mac without Peter Green. They are quite different. I'm a blues aficionado so the former is my favorite composition of the band's members.