a pom pom dance is a Cheerleading dance with pompoms all the time

Shake Your Pom Pom was created on 2008-03-04.

Pom Pom - film - was created on 1984-02-22.

barbie pom pom squad

No. Many people believe that pom-poms should have a "plural-plural." But, "pom-poms" is the same, whether it is one set or a hundred sets. If there are two or more pom-poms its just pom-poms.

As a comparison, it would be like asking if one dog is a dog should two dogs be referred to as dog dog.

Also, the singular of pom-pom is pom-pom. It comes from the French word pompon. Although some people will tell you that the singular is just "pom," this is not true. You can have one pom-pom, or many pom-poms.