Yes, the word residence is a common noun, a word for the abode of anyone, anywhere.
A proper noun is the name of a specific person, place, thing, or a title; for example:
- The Byrdcliffe Artist in Residence Program, Byrdcliffe Art Colony, Woodstock, NY
- Residence Street, Moscow, ID or Residence Street, Enterprise, OR
- Residence Inn by Marriott, Extended Stay Hotels, Bethesda, MD
- "Residence on Earth", poetry by Pablo Neruda