You can change your online status on Discord and customize your visibility to friends and other users. You can also set a custom status in the same section of your Discord profile.

The company’s “Rich Presence” SDK enables game studios to hook their games into Discord to provide player status information as well as options to join or watch your friends.

Gaming chat app Discord is quickly becoming a full-fledged social network. The latest move toward this is the ability to set a status for yourself and let folks know what game you're playing. More ...

Just keep in mind that your PlayStation profile must have both its PSN Online Status and Now Playing visibility options set to "Anyone" for it to work with the Discord activity display.