Is many is a proper noun?

No, the noun 'many' is a common noun, a Word for a large indefinite number.

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

• Many, LA 71449 (pop. 2700) or Many Farms, AZ 86538 (pop. 1500)
• Many Waters Road, Bristol, VT
• Many Forks Farm, Clarksburg, MA
• "Many Happy Returns", 1986 movie with George Segal, Ron Leibman
• "The Many Deaths of the Black Company", a novel by Glen Cook

The Word many is also an adjective and an indefinite pronoun.