You need to have BeamMP Client downloaded and installed.
You can find out all about it in this guide on how to set it up and even create your own server! here

• Simply Right click on BeamNG.Drive and select properties and in the general tab, locate launch options.
  
• Next type in the file location of where you have BeamNG.Drive and match it to your drive letter+location. As you can see mine is E:\BeamMP-Launcher\BeamMP-Launcher.exe %command% copy this and just change it to where you have it installed. Typical Default location is: "%appdata%\BeamMP-Launcher\BeamMP-Launcher.exe %command%" if you installed it elsewhere but don't remember, right click on your BeamMP shortcut (either start menu or desktop icon)and select open>more>open file location and then right click on the shortcut and select open file location again (for Windows 10 and via start menu) If doing from shortcut from desktop you should be able to just right click and select open file location just the once.

• Now you can close this and launch BeamNG.Drive via Steam.

As you can see Steam reports you playing BeamNG.Drive.
It also updates that your playing Multiplayer on what map and in what vehicle your currently using


And the multiplayer option is there and won't give you the error message about not running BeamMP

Edit: From user - SlaynHollow " getting an error like "afdabrikman" just rename your "\AppData\Roaming\BeamMP Launcher\BeamMP-Launcher.exe" to "\BeamMP-Launcher\BeamMP-Launcher.exe" in BOTH the Steam Properties settings for BeamNG.Drive its self, AND also the ACTUAL file name for the "BeamMP Launcher" FOLDER, it NEEDS to have a "-" inbetween BeamMP and Launcher or else you get stupid syntax errors. "

Steam user: Cadillac V-Series.R LMDh 5.5L V8 for their comment on this post that I found when I was looking to see if this was possible.

The thread can be found here for those who are curious

I've just recently created my own server. It's up from Friday - Sunday unless it gets busier.
I've recently made a discord server you are free to join and lemme know how the server runs.

If your not into Discord and such, that is fine. Just search for "Bacon's Server |AU|"
And you should find it.
Note: If the server doesn't pick up traction, the server and discord server will be removed in January 2024

Update: 6/12/2023 - Discord has been deleted.
Update: 6/2/2024 - Server has been deleted