Do you capitalize a noun when it refers to proper noun?

In most styles, when a common noun becomes part of a proper name as a distinguishing title or becomes the name of an official or institutional position, the noun is often capitalized.

* Capitalization: She is the Chief Executive Officer of the company.

* Common: Sarah Miller, who you met last week, is the new chief executive officer of the company.

* Capitalization: Dr. Smith is the department head.

* Common: Dr. Smith, the department head, is attending the conference.

However, there are exceptions where the common noun loses its independent meaning within the proper title and is no longer capitalized.

* Common: the king of France

* Proper, no capitalization: the King of France