From the comments;
The Tenth Doctor JPDisquses • 3 days ago
On the board where Q “drops” are posted, there is an elaborate “trip code” and login credentials that lets people know it’s supposedly Q posting.
Jake Hanaran did a podcast series called Q Clearance that does a deep dive into who started Q, how he lost it, who took it over, etc.
He can get a little circuitous at times, but there’s excellent information in it.