You hold the copyright to your thesis. Some students include the copyright symbol © with their name on the cover sheet to indicate that.
After uploading your thesis/dissertation and submitting information about it, you will be presented with the option of having ProQuest register it with the US Copyright Office. Harvard University does NOT recommend this option. You already hold the copyright by having authored your thesis and putting it in tangible form, and you will avoid paying a fee to ProQuest for that service.
Harvard University recommends that you choose Traditional Publishing. When choosing this option, theses will be available online as open-access publications through Harvard’s institutional repository (IR), DASH. DASH ensures the availability, longevity, and functionality of your thesis.
Creative Commons licensing: Currently, Harvard students cannot choose a CC license during submission via ProQuest. But! Although the non-exclusive license agreement for DASH is not CC-BY, it is essentially the same set of rights.
If you have more questions on copyright/licensing for your thesis, you can contact the Harvard Office for Scholarly Communication: osc@harvard.edu.