Unable to create additional private channels

Q: I have problem creating more private channels. Is there a limit?

A: The maximum number of private channels is 30, including deleted ones. (Refer: https://docs.microsoft.com/en-us/microsoftteams/limits-specifications-teams)

You can check under Manage Team > Channels. Teams admin will not be able to see or delete those under "Deleted".

After you delete the channel, you can no longer create a new channel with the same name. 

The workaround is by restoring a deleted channel, renaming it to something else, and then deleting the channel again. The previous name is then available for use.