According to the Traditional Ballad Index, in the original poem by the Rev. Henry deLafayette Webster, the girl was Bertha, but when Joseph Philbrick Webster set it to music, the name was changed to Lorena because a three-syllable name was needed.
I haven't found the original poem yet.

"Way Down in Alabama" has many faces. It may be a folk revision of Lorena (I presume you mean the Smyth County Ramblers version), but several songs take that name or have that line and similar subject. Perhaps related to the blackface "Ma Angeline" or the minstrel song "The Gal with de Blue Dress On" (see American Memory) etc.