Is monkey a proper noun

No, the noun monkey is a common noun.

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

• Wild Futures' Monkey Sanctuary, Looe, UK
• Monkey Business, 1931 Marx Brothers or 1952 Cary Grant & Ginger Rogers
• Monkey Road, Elgin, TX
• The Monkey Bar, New York, NY