Yes you can, see here:
Rename github repo
If I understand you correctly you want to rename your git repository eg xyz.git to xyz1.git and then have all the git repositories that link to that repo link to the new name automatically?
As far as I know this isn't possible. Each repository is self contained and keeps a list of locations it links to. If one of those locations changes its name the link would be broken. Each repository that references the changed name would need to update its link.
But then, the same would happen if you deleted a repository and recreated it under a new name....
Just realised you were specifically talking about GitHub and not git in general, sorry - should learn to read the entire question like my school teachers said. The answer still stands, with the addition that you can change the name in GitHub from the Admin page.