Lots of 19th century (and earlier) Cherokee people didn't have a surname; in those cases we use the tribe name, so the LNAB is "Cherokee." "Little Buzzard" is a given name. During the 19th century, when people began asking for surnames, children sometimes used their father's given name as a surname, so the daughter of Little Buzzard would be called Chah wah you kah Little Buzzard.
Wilson-41495 looks fine. Her mother is fine, but her mother's parents should be listed as
Father: Proper First Name: Little Buzzard Preferred name: Little Buzzard, Last Name at Birth: Cherokee
Mother: Proper First Name: Nelsey Preferred name: Nelsey, Last Name at Birth: Cherokee
They are both listed on the 1851 Drennan Roll. Their daughter's name is spelled Chah wah you kah on that roll.
I can't identify Little Buzzard and Nelsey on the 1835 Cherokee census, he is probably listed with his name in Cherokee, but yes, that couple would have come to Indian Territory on the Trail of Tears.
I can't connect Thomas Wilson to any parents. He was apparently born after the 1851 Drennan Roll and died before the Dawes roll. It's also possible he is on the Drennan with a Cherokee name, but the 1880 census lists him as 27 years old so born in 1852 or 53.