I suspect that your best friend's parents may have been fans of a soft-rock duo named "The Captain and Tennille" who were popular back in the 1970s. ("Popular", that is, for folks who thought "Muskrat
Love" really rocked, I suppose).
The name "Tennille" (like the song, "Muskrat
Love") doesn't seem to have appealed to a very large proportion of the U.S. population outside of those parents naming new babies in the 1970s. A quick check of the Social Security Administration's actuarial notes for the top 1000 baby names for each decade revealed that the name "Tennille" ranked #952 in the 70's -- it does not appear on any previous or subsequent decades' top 1000 lists.
The name "Tennille" seems to be a surname of French origin, which can also be found among a number of old families in American's Deep South.
Toni Tennille (the prettier half of The Captain and Tennille duo) was born in Alabama. There is also a town named "Tennille" in the state of
Georgia.
It's not unusual for people to give an pleasant-sounding surname to a baby as that child's first name. The name "
Taylor", for instance, this year rose to the number seven position among most popular baby girls' names in the U.S.
Perhaps you might find out more about the name by visiting and posting an inquiry on the Tennille Family Genealogy Forum at:
http://genforum.genealogy.com/tennille/
Good luck! And come back here and tell us about the name if and when you find out more.
-- Nanaea