When used in sentences, it is generally enough to just use "Dr. Harvard" without being too verbose. Harvard University is a world-famous institution, and no one can understand it. When the school name is used with a degree, the school name is used as an adjective.

For example:

He is a doctor at Harvard University.

He has a doctorate from Harvard University on his resume.

Other schools and degrees (even majors):

John is an MBA from Stanford University.

She received a doctorate in economics from Columbia University.

Of course, if you want to be more "written", you can also use the "degree" in the "school name" (doctor of Harvard) to express it.