For PMs, the line corresponding to the message should be highlighted for better visibility. Similarly, if someone mentions your player ID, or your username, the text that mentions these should be highlighted so that you are made aware that someone is talking about you. For example, someone may have a question about the truck you're driving, and in busy areas it's very easy to miss messages that are directed towards you.
Image example:
All in all, this is a good suggestion, but I personally think it goes hand in hand with "redeveloping" the entire chat system which was suggested a while back. (see this thread) I'll add other things I'd like to see.
Language channels
Similar to what we have on the TruckersMP Discord, I'd like to see language channels that a user can "subscribe" to. For example, if I'm subscribed to the French language channel, I can only write French. This would also help with filtering out server announcements from my chat that I don't understand.
Disabling repeated messages
Many users seem to think it's okay to repeatedly spam their VTC advertisements in busy areas, having a feature where by sending the same or similar message in a short time frame times you out from the chat would improve the experience for many users, similar to how Twitch chat operates.
Chat configuration options and readability
As a person who owns an ultrawide monitor with a fairly high resolution, I find it difficult to read the chat due to the small font size. Giving users the ability to customise the chat interface with different font options (please no Comic Sans!) and font sizes would really help in improving accessibility. I'm aware this is possible through mods, but having a native option would be so much better. Adding a timestamp option would also be very nice.
"Modular" chat interface
Being able to move, resize, hide the chat similar to the player tab list.
Server announcements and in-game warnings
Highlighting server announcements similar to the suggestion above would make them more prominent. I've found in many instances of night time driving where I could not read the message without looking up close due to the nature of the dark red font against night environments.
Fixing some of the old chat bugs
If you have something in your clipboard and type the letter V, it sometimes pastes what you have in your clipboard into the chat.
Pausing the game with the chat open leaves you no option but to ALT+F4 and restart your game as there's no way to close it.