Currently we are using 
LINKSYS USB ETHERNET ADAPTER - GIGABIT USB 3.0 (Model-Nr. USB3GIG-EJ)
These work as plug-and-play with debian10. 

To assign a permanent name for the network adapter (e.g. as listed by 'ip a' command) one needs to edit/create
the file 
/etc/udev/rules.d/70-persistent-net.rules 
and add for each adapter:
SUBSYSTEM=="net", ACTION=="add", ATTR{address}=="XX.XX.XX.XX.XX.XX", NAME="usb_eth0"

Then reload the rules with:
sudo udevadm control --reload-rules

The device with the given MAC address will now always be loaded as "usb_eth0".