Full moon names by season (Northern or Southern Hemisphere):
After the winter solstice:
Old Moon, or Moon After Yule
Snow Moon, Hunger Moon, or Wolf Moon
Sap Moon, Crow Moon or Lenten Moon
After the spring equinox:
Grass Moon, or Egg Moon
Planting Moon, or Milk Moon
Rose Moon, Flower Moon, or Strawberry Moon After the summer solstice:
Thunder Moon, or Hay Moon
Green Corn Moon, or Grain Moon
Fruit Moon, or Harvest Moon
After the autumnal equinox:
Harvest Moon, or Hunter’s Moon
Hunter’s Moon, Frosty Moon, or Beaver Moon
Moon Before Yule, or Long Night Moon

There are usually three full moons in between an equinox and a solstice, or vice versa.
Seven times in 19 years, four full moons fall in a single season. In that case, the third of a season’s four full moons is also called a Blue Moon. The last Blue Moon by this definition happened on August 21, 2013.