Is "Governor of Kentucky" a Proper Noun? Yes.

Yes, "Governor of Kentucky" is a proper noun phrase.

Why

• It refers to a specific, unique office within a specific sovereign jurisdiction (the Commonwealth of Kentucky).
• It functions as a title + office combination, akin to "President of the United States" or "Mayor of Chicago."
• When used with the officeholder's name (e.g., "Governor of Kentucky Andy Beshear"), it is a formal title—always capitalized.
• Even standing alone ("The Governor of Kentucky announced..."), it denotes a particular office, not a generic category.

Contrast with Common Noun

"A governor" (common noun) = any person holding a gubernatorial office.
"The governor" (common noun phrase with definite article) = context-dependent reference.
"Governor of Kentucky" = unique, named entity = proper noun.