For example:
Person A is working in the X branch.
Person B is working in the Y branch.
Person C pulled the codes from Person B's branch by rebasing and git fetch.
Because it wasn't doing the fast-forwarding.
Now the problem is whenever Person A and Person B commit and push their codes into their branches and in GitHub, it shows that it pushed into that Person C's branch.
Can anyone please explain why it's happening?
When you git push with no further arguments, you push to the local branch's remote tracking branch", sometimes also called the upstream branch. For example, branchA might track origin/branchA. But it does not have to be so. branchA could track origin/branchC.
You can see what all your local branches are tracking with git branch -vv.
branchA 24c27e21 [origin/branchA] Description of the last commit to branchA
The tracking branch is usually set up automatically, this can be controlled with branch.autoSetupMerge. It can also be set manually when creating a branch with git branch --track and changed with git branch --set-upstream-to.
Note that this is all part of the local repository. PersonC should not affect how PersonA nor PersonB tracks.
The other way you can push to a differently named branch is to simply tell git push to do so.
git push origin branchA:branchC
This says to push branchA to branchC on the origin remote.