Joanne:
I also think that Christine hated being named "Perfect" and that contributed to her changing her name to McVie. I doubt that she ever really considered keeping her own name, even professionally, despite the fact that she had an established reputation with that name.
*FACT*
Moz:
About Chris officially joining, Mick says: "Before we went on the road in America with that album [Kiln House], we asked her to join."
Chris: "Ten days later I was in America, in New Orleans. I'd never been to America in my life... with Fleetwood Mac! I couldn't believe it."
Mick: "She learned the songs in New Orleans before the first show."
That sums it up nicely, and is about where SteveMac and I placed it - just after the Kiln House project, and just before the performance at The Warehouse. Brings everything to full (explanatory) circle in regards to aleuzzi and my earlier exchange to boot.
Moz:
The first show after the recording of Kiln House was on August 1 at the Warehouse Cafe in New Orleans.
If Aug 1 can be confirmed, then Chris was technically a member either in mid-to-late July, or at the beginning of August per that first performance (as is often cited). In the same vein, it's hard to say whether Fleetwood Mac was "formed" in July of 1967 during early rehearsals, or on August 13 per their first official performance at Windsor. [I lean toward the latter]
Wouter:
Oh Well wasn't part of the original release (UK) of Then Play On. Thus one could say that Jeremy didn't take any part in the album. 
Good point Wouter! Technically it could be argued Jeremy was completely absent from the TPO release. Wow.
OTOH :: Oh Well was recorded and released as a single during the same period (and sessions), so it's kind of hard to think of TPO as being
sans Oh Well. The Yanks sure never saw it that way, and they are after all what came to really matter after TPO was released! [-- with the falling off the radar the band took in the UK and much of Europe after Green departed, and their gradual embrace on this side of the Atlantic particularly after the release of Then Play On. Some in Europe were even abandoning FM shortly
after TPO was released and
before Green left, claiming the Mac had "sold out" their blues roots!]