Let us first start on what exactly a 'Full Moon' is. A Full moon is a lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun.
Now that that is out of the way, let me tell you that besides having an Astrological Moon Phase, the Full Moon itself has many other names that are separated by month, which is what I will be telling you here, but before this, I will tell you where these name originated.
The full moon names dates back to the Native Americans of what is now the Eastern and Southern United States. The names are applied to each month in which the Full Moon happens. There are variations in the Moon names but the same ones were current throughout the Algonquin tribes from New England to Lake Superior. European settlers followed that custom and created their own names as well. However, since the Lunar Year is only 29 days long, the moon dates shift from year to year.
[The Full Moon Names]
[Early-Late Winter -Winter Solstice-
January: Wolf moon.
(Other names: Moon After Yule, Ice Moon, Old Moon)
February: Snow moon
(Other names: Hunger Moon, Storm Moon, Candles Moon)
March: Storm moon
(Other names: Crow Moon, Crust Moon, Sugar Moon, Sap Moon, Chaste Moon, Death Moon, Worm Moon, Lenten Moon)
[Early-Late Spring -Vernal Equinox-]
April: Seed moon/Pink moon
(Other names: Sprouting Grass Moon, Fish Moon, Growing Moon, Waking Moon)
May: Milk Moon
(Other names: Corn Planting Moon, Corn Moon, Hare Moon, Flower Moon)
June: Mead Moon
(Other names: Honey Moon, Rose Moon, Hot Moon, Planting Moon, Flower Moon)
[Early-Late Summer -Summer Solstice-]
July: Hay moon
(Other names: Thunder Moon, Mead Moon)
August: Corn Moon
(Other names: Red Moon, Green Grain Moon, Lightning Moon, Dog Moon)
September: Harvest Moon
(Other names: Corn Moon, Barley Moon, Fruit Moon)
[Early-Late Fall -Autumnal Equinox-]
October: Hunter's Moon
(Other names: Travel Moon, Dying Grass Moon, Blood Moon, Harvest Moon)
November: Beaver Moon
(Other names: Frost Moon, Snow Moon, Hunter's Moon)
December: Oak Moon
(Other names: Frost Moon, Winter Moon, Long Night's Moon, Moon Before Yule)
I will post a description of each later.
I hope this is able to help you.