Remote and local repo containing folder with different name but want to track them

[mostafiz.buet10.ss]

Suppose I have a local repo having a directory X. I want to push this in a remote repo directory with different name without changing the name in local. Suppose in remote repo, the directory name should be Y. I always want keep track the contents of directory X of local repo with directory Y of remote repo. FYI All other directory of remote and local repo are same.