Choctaw Nation of Oklahoma

I am hunting information on Calvin Gibson and his wife Nancy Unknown, their children were:
Eliza Gibson, Lawrence, Bell, Bloodworth- roll # 13627
Martha Gibson, Colbert, Anderson-roll # 13979
Louisa Gibson, Wells-roll # 13624
John ‘Johnnie’ Henry Gibson-roll # 13623
Douglas Gibson-roll # 13630

I am the great grandaughter of Eliza Gibson Bloodworth
I would love to know how Calvin Gibson a full blood Choctaw got the name Gibson for a last name. Calvin’s wife Nancy was full blood Chickasaw.
I guess this is where I will start my research.
Thank you so much for any information.