I'm surprised you can't find much because I immediately found some very interesting information. It seems clear that the name Wynema entered the "general" American name pool because of the novel Wynema, A Child of the Forest
by S. Alice Callahan
, originally published in 1891 and available in reprint from the University of Nebraska Press. It is considered the first American novel written by a Native American woman:http://unp.unl.edu/bookinfo/3286.html
was a member of the Muskogee or Muscogee nation of Native Americans (often called "Creeks"), and the heroine of her novel was an Indian girl named Wynema Harjo. Harjo is a fairly common surname in Oklahoma and is one of the few surnames from a Native American language to be in regular use in the USA. Since Harjo is a real Muskogee name, it's possible that Wynema is also. However, it's also possible that Ms. Callahan
invented the name herself. One would have to consult an expert in the Muskogee language to be sure. In any event, it is clear from the references to women named Wynema found on the Web today that Wynema has been frequently used by persons of both Muskogee and Cherokee
ancestry in Oklahoma since the novel was published. So it seems to either be a real Muskogee name, or at least one that's been adopted by the Muskogees as the name of a fictional heroine from their group.