Stream IDs are not magical in any way and can be manually or automatically created and reused.
Use &push=STREAMID to publish a video and &view=STREAMID to remotely view it. If you don't manually specify a stream ID, VDO.Ninja will sometimes generate one for you. You can reuse the generated stream ID if you wish.
Stream IDs only exist when they are actively used; once you stop using a stream ID, it no longer exists until it is used again.
Additional technical details of stream IDs
When in a group room, a stream ID can only be accessed from within that same room, unless transferred to a new room by the room's director
To make up a valid stream ID of your own, choose something with less than 51-characters of length and ensure it's AlpHaNuMerIc-only.
A stream ID must not already be in active use, else you will be provided with an error stating this.
This isn't the case when using a password however, as the password AND the stream ID must be the same in this case for the stream ID to be considered already in use. So, you technically can reuse the same stream IDs, changing only the password, if security is a concern. Even still, you should try to keep stream ID's confidential and change them when appropriate.
You can use the &label property to give a name to a stream, rather than using a stream ID to do the same. Using this strategy of using securely-named stream IDs, while using labels to assign a name to a stream, will improve security and unlock new options, like lower-third display name overlays.
A director does have a stream ID, and they can be manually assigned to a director in the same way they are assigned to any publisher.