Companion Notification icons in left of screen appears when they need to talk with you in the Party Camp.

Disable Companion Notification

Unfortunately since it's important to talk with your companions in party camps, you can not directly disable notifications but you can disable it if you don't care about other icons in your screen.

• Open Menu and go to Settings > UI > HUD Settings and choose Off for HUD.

This will disable everything in your screen except the mini-map and your current quest.