I received a note from Mr. Jeff Beacham who kindly provided me with a list of such names. I cannot, however, vouch for their authenticity, but here they are:
Month ALGONQUIN OJIBWA -------------------------------------------------------------------------- 1. January WOLF MOON GREAT SPIRIT MOON 2. February SNOW MOON SUCKER SPAWNING MOON 3. March SAP MOON MOON OF THE CRUST ON THE SNOW 4. April SEED MOON SAP RUNNING MOON 5. May FLOWER MOON BUDDING MOON 6. June STRAWBERRY MOON STRAWBERRY MOON 7. July BUCK MOON MIDDLE OF THE SUMMER MOON 8. August STURGEON MOON RICE-MAKING MOON 9. September CORN MOON LEAVES TURNING MOON 10. October RAVEN MOON FALLING LEAVES MOON 11. November HUNTER MOON ICE FLOWING MOON 12. December COLD MOON LITTLE SPIRIT MOON 13. Varies BLUE MOON BLUE MOON