The Rocket League Private Match not working is an ongoing issue that players have been facing for a long time now, but fortunately, there is a quick fix when the issue occurs. If you haven't experienced the issue you're lucky, because the issue ends up putting players in servers other than their private ones.
Rocket League Private Match Not Working: Quick Fix
In order to fix the Rocket League Private Match issue, players should try to delete the match and try again. If it happens a second time, players should repeat the same process. Players on Reddit who have encountered this issue suggest this fix, and it has worked, reportedly, most of the time.
It appears that setting up the private match under the same name is part of the solution, so for now making the second and third private lobbies should contain that same information (or as close as it can be, such as adding a number or additional letter to differentiate). At large, the issue may drop players into another game. It's a weird issue, but it seems to only be causing this and not a larger game crashing bug.
Psyonix has responded to multiple threads on Reddit exclaiming that they are looking into a fix. The issue seems to be a Psyonix issue, and while players wait for a more official solution the delete and recreate is the most effective workaround at this time. It does not look like the issue will be fixed as Season 3 of Rocket League continues.