A name is a proper noun when it's the name of a specific person, place, or thing.
A name is a common noun when it's a general Word for a person, place, thing. The Word 'name' is used in a number of contexts, for example:
- When asked, "What is the name of the city with the Eiffel Tower?" "The Eiffel Tower is in Paris." The 'name' Paris is a proper noun, the name of a specific city. The noun Eiffel Tower is also a proper noun, the name of a specific thing.
- When asked, "What is the name of that pastry?" "That's called a turnover." The 'name' turnover is a common noun, a general Word for any of that type of pastry.