Ping microphone not recognized?

Which has only one jack connection.

As soon as I insert my microphone, it is recognized as a headphone.

Is it possible to change this technically or something?

Incidentally, I use Linux.

Does your laptop have nothing more than just a jack connection?

Only one

Check if this is not a connection for a headset. Since these connections have 3 or even 4 (stereo) lines / contacts, a 2-pin connector (micro or headphone) can give / receive the wrong signal depending on the position.

Usually a laptop should have several…
So at least two.

I think that the jack of your laptop for headsets is a so-called combo jack, in which the micro + headphone connections run over a plug. - See your user guide.

To connect only one microphone you need a suitable adapter, like this: https://www.amazon.de/...00KSV8YCM/