Here you can read how to disable chat in Diablo Immortal completely, and how to change its settings and the way messages are displayed.
When you open the game menu, you will see the Chat tab. Here you can turn chat on and off depending on your preferences. It's a good idea to scroll down the page first to decide the size of the chat window - but you can't change its position.
The first items on the page are the channels visible in the chat. If you want to reduce the number of messages, mark only the channels that interest you - e.g. messages from friends or from the clan. Leaving the My Log option will cause the game to resemble previous Diablo games - information about the collected equipment or experience will be displayed in the chat window.
If you uncheck all items - channels, the chat will stop: you can still see messages that have been recently sent. To get rid of the chat box completely, you have to restart the game.