When I plug my headphone into my Manjaro machine, although it can play sounds, it doesn’t show up in the microphone devices menu.
To fix this, I create and edit the following file:

/etc/modprobe.d/alsa-base.conf

Add this line to the end of the file:

options snd-hda-intel model=dell-headset-multi

After reboot, my headphone can be selected in the microphone devices menu.

This method also works on other linux distros such as Ubuntu.