Can you change your last name based on a domestic partnership?

Usually no, not solely on a domestic partnership. You would have to file a legal name change.

One exception is when registering a domestic partnership with the State of California. One or both partners can change their middle or last names on the Declaration of Domestic Partnership form as part of the registration. Information concerning this name change process can be found in California Family Code sections 298, 298.5 and 298.6.