Here is a solution:

You can hide the icon in menu bar by executing the following command in terminal:
defaults write com.displaylink.DisplayLinkUserAgent ShowMenuBarIcon 0

To show the icon in menu bar please execute the following command in termina:
defaults write com.displaylink.DisplayLinkUserAgent ShowMenuBarIcon 1

Note: Application restart might be required for these changes to take effect.

I can confirm I have applied this and it works.

I think this is a really important. Before the app / driver worked in the background. Karabiner the keyboard app does this well.

I'd like to chime in. Would love this, too. I only want items there with which there really is the need to interact on a regular basis. Imho it would make sense to have DisplayLink show up in the system settings instead/as well.

Agreed. I have so many icons in my menu bar, and this one does nothing important and yet I can't remove it.

Agree with the OP sentiment. If it helps, I've used Hidden Bar (https://apps.apple.com/gb/app/hidden-bar/id1452453066?mt=12), a free app that allows you to hide multiple seldom used icons. Other similar apps are available. Works on Big Sur at the time of writing.

Agreed! This icon takes up space with next to zero function and takes p space from other more relevant icons that could be useful. Please allow the option to hide/remove it without the programme quitting.

This.