if by any chance it's a first-name version of the surname Rhyne (pronounced the same way). This is a well-known surname in parts of western North
Carolina and eastern Tennessee.
Rhyne goes back to the
German surname Reinau. The Reinau family came to the US (Pennsylvania) before 1750 and moved south a half-century later. Somewhere during that time the name was modified to Rhein,
Rein, and Rhyne (the name that lasted). So why not one step further to Ryne, as a FIRST name? Using family surnames for first names was/is quite usual in the southern US.
Just a theory, mind you.
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Da.