Little is common among Old Regular, United and (I think) Separate Baptists as well, and I think it is more common in the Appalachian mountains than elsewhere."Little" in a church name is most likely used sort of in the sense of "insignificant (to the world)" and perhaps an expression of humility or a small beginning. "Little Hope" was, I thought, used exclusively among the Primitive Baptists, until I saw a sign many years ago for a Southern Baptist church near Canton, Texas called
Little Hope Baptist Church. On the other hand, I have seen several
Little Flock Baptist churches among Southern and Missionary Baptist. I wouldn't be surprised if there is some commonality of when these churches were organized and named. (IOW, I wouldn't expect to see too many Southern and Missionary Baptists organized in the 21st century to attach
Little to their names.)
I think every Baptist church I have seen with
Greater in the name was an African-American Baptist church. I think rsr's explanation is generally correct. On the other hand,
Greater New Hope in Sherman's name change coincided with a change in location, which might speak more to aspirations (there is at least no mention of a church split).