Ludema is not of
Cherokee origin. Versions of it have been used in Appalachia since the 1700s. It has many variations of spelling, such as Loudema, Loudemia, Ludemia, Lodemia, etc.
My personal belief is that the name originated as a variation of Laodamia, a name from classical Greek mythology about the Trojan War, probably coming from fairly illiterate people back in the 1700s hearing
Homer read aloud and assimilating the name they heard to sounds they were more familiar with.
For a reference to the original Laodamia see:
http://www.stanford.edu/~plomio/laodamia.html