Is dome a common noun

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

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

• Dr. Dome, character in DC Comics
• Half Dome, Yosemite National Park, CA
• Dome of the Rock, Jerusalem, Israel
• Dome Appliances, mfg. by HE Group Pty Ltd.
• "Under the Dome" a novel by Stephen King