General Medieval

Jan: Wolf Moon,  Stay Home Moon,  Moon after Yule

Feb: Storm Moon,  Ice Moon,  Snow Moon

March: Plough Moon,  Wind Moon,  Lenten (lengthening) Moon

April: Budding moon,  New Shoots Moon,  Seed Moon

May: Mothers' Moon,  Bright Moon, 

June: Mead Moon, Horse Moon, Dyan Moon,  Rose Moon

July: Claiming Moon,  Wyrt or Herb Moon,  Mead Moon

Aug: Dispute Moon, Lynx Moon, Grain Moon

Sep: Wine Moon, Song Moon, Harvest Moon

Oct: Hunter's Moon,  Blood Moon.  Seed Fall Moon

Nov: Mourning Moon,  Darkest Depths Moon,

Dec: Oak Moon,  Full Cold Moon

Chinese

January: Holiday Moon

July: Hungry Ghost Moon

February: Budding Moon

August: Harvest Moon

March: Sleepy Moon

September: Chrysanthemum Moon

April: Peony Moon

October: Kindly Moon

May: Dragon Moon

November: White Moon

June: Lotus Moon

December: Bitter Moon 

English Medieval

January: Wolf Moon

February: Storm Moon

March: Chaste Moon

April: Seed Moon

May: Hare Moon

June: Dyan Moon

July: Mead Moon

August: Corn Moon

September: Barley Moon

October: Blood Moon

November: Snow Moon

December: Oak Moon

Northern Hemisphere full moon names by month:
January: Old Moon, Moon After Yule
February: Snow Moon, Hunger Moon, Wolf Moon
March: Sap Moon, Crow Moon, Lenten Moon
April: Grass Moon, Egg Moon, Pink Moon
May: Flower Moon, Planting Moon, Milk Moon
June: Rose Moon, Flower Moon, Strawberry Moon
July: Thunder Moon, Hay Moon
August: Green Corn Moon, Grain Moon
September: Fruit Moon, Harvest Moon
October: Harvest Moon, Hunter’s Moon
November: Hunter’s Moon, Frosty Moon, or Beaver Moon
December: Cold Moon, Moon Before Yule, or Long Night Moon

Southern Hemisphere full moon names by month:
January: Hay Moon, Buck Moon, Thunder Moon, Mead Moon
February (mid-summer): Grain Moon, Sturgeon Moon, Red Moon, Wyrt Moon, Corn Moon, Dog Moon, Barley Moon
March: Harvest Moon, Corn Moon
April: Harvest Moon, Hunter’s Moon, Blood Moon
May: Hunter’s Moon, Beaver Moon, Frost Moon
June: Oak Moon, Cold Moon, Long Night Moon
July: Wolf Moon, Old Moon, Ice Moon
August: Snow Moon, Storm Moon, Hunger Moon, Wolf Moon
September: Worm Moon, Lenten Moon, Crow Moon, Sugar Moon, Chaste Moon, Sap Moon
October: Egg Moon, Fish Moon, Seed Moon, Pink Moon, Waking Moon
November: Corn Moon, Milk Moon, Flower Moon, Hare Moon
December: Strawberry Moon, Honey Moon, Rose Moon