DisplayLink uses DKMS to build and install the evdi kernel module from sources. This is the same mechanism that many other vendors, e.g. Oracle for VirtualBox use.
Unfortunately, this means that it is not possible to use the driver and the device just after installation, because modules that are built during the process have no signature, and therefore will not be allowed to load.
Option 1: Benefit from the automatic signing by dkms package
Since Ubuntu 18.04 signing modules is handled automatically by dkms package, remember to reboot to finalize
Option 2: Disable secure boot
Option 3: Sign evdi kernel module manually
The process of signing will have to be repeated after every kernel upgrade, or after upgrading to a newer version of DisplayLink driver.