This is an object of high and strong social significance in a certain culture. The name in its actual language is untranslatable, and carries a wealth of meaning.
We can call it a "Chastity Stick."
It is customary for young men and women to be chaste before marriage. When they are courting there is even a prohibition on holding hands. Instead, the "Chastity Stick" is used. The young man holding one end; the girl, the other.
The example shown is a rather detailed carving, usually intended for a couple who are near marriage age. Younger girls and boys would get one with less erotic symbolism. Even as simple and uncomplicated as a twig with a burl, or even a spoon.