The pagan festival has got nothing to do with Easter. It is celebrated on 21 March, the Spring solstice, while the religious festival called Easter in this country is celebrated on the first Sunday after the first full moon occurring on or after the vernal equinox. So several weeks later.
The fact that the early English preferred to use the local name for the pagan spring festival for the Christian religious festival as well is purely incidental and a matter of local custom and practice. Other countries use a version of the name of the Jewish festival of Passover, that also happens at this time. Pasque, in French or Paschal,(an adjective) in English.