Mobile:
Go to Messages tab
Select Group Message to change picture
Click on group message name at top of screen
Click Change conversation name or picture
Click on current/default Group Message photo
Select from two options: Camera & My Photos
Camera: Take a picture with the camera on your device
My Photos: Select existing photo from your device
Click Save in top right corner
Web:
Go to Messages tab
Select Group Message to change picture
Click 3 dots (⋮) in top right corner
Click Change conversation name or picture
Select picture to change
Add new picture
Click Save