To its essence, an ID allows interested parties to track something over time.
If you add additional meanings to an ID - e.g. the parent project as Jira does, or the kind as in ServiceNow - these can become outdated over time, and deceiving.
I'd say it's ok to change the "external name" as this other metadata changes over time (project name, bug, task, story, whatever...) but make the obsolete synonyms redirect to the currently active name.