The correct command that can change both the username and group name a file belongs to is 'chown'. The 'chown' command is used to change file owner and group in Linux. The 'chgrp' command is solely used for changing the group ownership of a file. The 'chmod' command changes the file permissions, and 'newgrp' is used to switch the current user's group. Therefore, 'chown' is the command that meets the requirement stated in the question.