Where I work many people use the same computer on the same account. We now use the shell instead of the GUI just for convenience.
The first time someone committed it
If you use a Windows system, the Git username and password is stored in a control panel. You can go to Control Panel → User Accounts → Credential Manager:Generic Credentials to delete it.
It seems that users credentials are being cached.
Go to your project, open .git/config
and remove the lines:
[credential]
helper = store
# or helper=cache
Check git-credential-store for more information.
Edit: OP mentions in the comments that this is happening in Windows, for which, the other answer is more relevant for removing the credentials from the Control Panel.