Why are the moon names different when they are within the same month?

Because of the nature of the lunar calendar versus the Gregorian calendar, sometimes there are two full moons in a month. The Gregorian calendar is the current solar model most of us adhere to, with months and days. But the lunar calendar is different, as it is made up of 29.5 days. That means that sometimes, lunar months--aka, moon cycles-- will overlap within a solar month. Hence, differently-named moons within the same month.