It’s not real and nor does it refer to fingers or your bum.

-ingen is a common suffix for towns in Baden-Württemberg. Tübingen, Reutlingen, Vaihingen, Villingen-Schwenningen are some of the bigger ones that come to my mind. But like half the towns are named -ingen.

So it’s more like Hinter-tupf-ingen if you want to lose the finger association.