No, monarch butterfly is a common noun, a Word for any monarch butterfly anywhere.
A proper noun is the name of a specific person, place, thing, or a title; for example:
- Thelma 'Butterfly' McQueen, actress
- Monarch Mountain, Monarch, CO
- Monarch Butterfly BiOSphere Reserve, Mexico (UNESCO World Heritage Site)
- Monarch Inn, Norfolk, VA and Butterfly Grove Inn, Pacific Grove, CA
- "Monarch: Butterfly"(stage four of "Monarch" series), by Aaron Pitters
