There are many potential reasons why you can't see an organisation site in Blackboard.
Managing site settings
If a site is "Private", it means that students cannot see the site but staff can access it.
This article describes how you can customise your Blackboard module and organisation sites.
If a Blackboard site is no longer needed or has been made accidentally, and you wish to delete the site permanently, it is possible to request this yourself by following these instructions
Yes, you can rename organisation sites completely and you can append differentiating text to module sites (e.g. Jan 2023 cohort).
Blackboard module sites are linked directly to the module SI code, so unfortunately the module code can't be changed in Blackboard.