Basing their hypothesis on a passage of the Venerable St. Bede, some claim that the Anglo-Christians adopted the name Easter from the name of a pagan goddess: Eastre in Anglo-Saxon; Eostre in Northumbrian. The name comes from the proto Indo-European root "aus" meaning "to shine" and "the east" (since the sun shines from the east). She is the infamous Ashtorah of the Old Testament, the one for whom poles were erected as signs of fertility. The kingdom of Austria comes from the same root since it is the kingdom of the east or the "austra".
The Catholic Church does not formally call the feast "Easter" but rather "Pascha" - a word derived from the Aramaic word for "Passover". Only English and Germanic lands use the term related to "Easter".
Some apologist claim that Easter comes from the Anglo-Saxon word "oster", meaning "to rise". This would be a convenient etymology since it avoids the pagan connotations.
I favor a third explanation. The Anglo-Saxons called the Spring equinox "Eostre". It was a astronomical description. Since pagans ceremoniously celebrate astronomical events as holy days, the natural phenomenon (the spring equinox as a "shining") and the religious feast (the goddess of fertility and light, Ashtorah) were indistinguishable.
Anglo-Saxons didn't borrow the name of a goddess for the feast of Christ's resurrection. They simply denoted it by the name of the natural phenomenon (the spring equinox), since the festival is calculated by using marking the equinox. It just happens that the name of the goddess and the name of the feast are etymologically connected. This would confirm the exact context of Bede's words:
"Eostur-month, which is now interpreted as the paschal month, was formerly named after the goddess Eostre, and has given its name to the festival."