There are two text messaging apps on your Samsung Galaxy phone. If you're using Google Messages (the app icon with 3 horizontal bars), there aren't many options except you can choose a white or dark background in its Settings > Choose theme.

Suppose you're using Samsung Messages (the app icon with 3 dots). In that case, you can customize the message background of each conversation window by following the steps below:

1. In a conversation view, tap the three-vertical-dot Menu button > Customize chat room.
2. Here，you can pick a custom photo or a specific color from the given options as the background.
   
   

For some reason my Samsung messages options (for customising chat/wallpaper settings) is all greyed out so I cannot select them. It happened after an AVG clean on my phone. I can't find anything anywhere that mentions these options being greyed out