Is heaven a common noun

Yes, the Word heaven is a common noun, a Word for any kind of heaven.

A common noun becomes a proper noun when it is the name of a person, place, thing, or a title; for example:

• Heaven Davis, singer, President of the Atlanta Blues Society
• Heaven Hill Farm, Vernon, NJ
• Heaven Street, Norlina, NC
• 'Kingdom of Heaven' (2005) Orlando Bloom, Liam Neeson