Upvote:4
According to the SCLC web site, it took about a year for the organization to form, in a series of meetings, changing name several times: in Jan 1957 it was the "Southern Leadership Conference on Transportation and Nonviolent Integration", in Feb 1957, the "Southern Leadership Conference", and, in August 1957, the "Southern Christian Leadership Conference", which it has remained ever since. Further details are in the wikipedia SCLC page and in its sources, and at the King Institute.
Google books shows that the term "Leadership Conference" was in wide-spread use in America in the first half of the 20th century, generically used in the names of ad-hoc committees within organizations such as the 4H club and churches of various denominations.
Of course the leading figure in the SCLC story, Dr. Martin Luther King, Jr., was a Baptist, as were many of the other participants; many of the early meetings were held in Baptist churces. So it makes sense -- a kind of sense -- that people might use the descriptive phrase "Southern Baptist Leadership Conference", even though I don't think it was ever an official title of an organizational predecessor of the SCLC.
Indeed, as T.E.D. comments, "Southern Baptist" usually refers to the "Southern Baptist Convention", a denomination that seems generally unsympathetic with the SCLC's program. This is in contrast, as Jon Custer commented, with "Southern Christian" which is simply a string of descriptive adjectives without any implication of organizational affiliation. (Other than with the SCLC itself, of course.)