And the name in fact is in the very deep roots the same as turpentine (Greek terebinthos), though whether the stuff is named for the tree or the other way around is unclear. The tree name passed through Latin and Old French to arrive in English in the late 14th century, while the material morphed into a feminine form in Latin and underwent even more sound changes in Anglo-Norman, including changing the -b- to -p- in early Middle English. Heading the other direction, the Greek word is apparently of foreign origin, possibly Cretan/Minoan. Either way, given mentions of it in the Bible, both Terebinthia in Narnia and the Terebithia that is bridged to are likely supposed to evoke the stuff.
"So they gave to Jacob all the foreign gods that they had, and the rings that were in their ears. Jacob hid them under the terebinth tree that was near Shechem." (Gen 35:4)