Once you begin an EdX course, the "View Course" button will change to "Resume Course". The "Resume Course" button remains as long as the course is still available on edX and will not change to show the course as completed.
To see your progress toward completion in the verified track you can view your course grading on the progress tab within your course. If the total column meets or exceeds the passing line then you have successfully passed the course.
If you are registered in the verified track and earn a certificate you may share this with others to show that you completed the course.