Is the word concern a common noun?

Yes, the Word concern is a common noun, a Word for any concern of anyone.

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

• Concern Mom Soar on Eagle Wings (childcare), Irvington, NJ
• Family Concern Ministries, Cleveland, OH
• Concern Worldwide (international charity)
• 'To Whom It May Concern' by Bob MacKenzie