Hiding your name helps, but it isn’t the same as being anonymous. If you post a photo of your setup, mention your town, or write in a style your friends would recognize, a stranger reading a Google result could still connect it to you. People in big fandom or game servers often share more than they would on a public forum, because the room feels like a clubhouse.
Timing matters too. If you leave the setting on and change your mind later, switching it off only protects messages you send from then on. Anything published while it was on stays visible until you delete that message in Discord. Even then, Discord warns that search engines may keep cached copies for a while.
Money talk is a good example of the risk. Discord’s public directory lists nearly 800 servers tagged cryptocurrency, about 1,400 tagged trading and more than 700 tagged finance. Plenty of people in those rooms mention what they hold, which exchange they use or how much they lost last week. That’s exactly the kind of detail scammers search for, and it’s the kind of post you may not want sitting under a Google result.
The simple rule: if you’d be uncomfortable seeing a post quoted on the open web, either opt out now or don’t post it in a Discoverable Server.