This was originally the surname of the singer
Toni Tennille, and became a given name because many people assumed it was her first name because she was part of the singing duo billed as "The Captain and Tennille". It is a real family name and was not invented to be a stage name. The Tennilles in the USA believe the name was originally French, which may be the case, but so far I haven't found it listed as a French surname in reference books. Dauzat's
Noms et prenoms de France lists Teneuille as a suname from a place called Theneuille, but gives no etymology for the place name.