Is the roller - skating rink a noun?

The compound noun roller-skate is a common noun, a Word for any roller-skate of any kind, anywhere.

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

• Harborena Roller Skating Rink Inc., Hoquiam, Washington
• Lenexa Supreme Roller Skates
• National Museum of Roller Skating, Lincoln, Nebraska