Says the Oxford English Dictionary (to which I cannot link).
Bede... derives the word < Eostre ... the name of a goddess whose festival was celebrated by the pagan Anglo-Saxons around the time of the vernal equinox (presumably in origin a goddess of the dawn, as the name is to be derived from the same Germanic base as east adv....). This explanation is not confirmed by any other source, and the goddess has been suspected by some scholars to be an invention of Bede's. However, it seems unlikely that Bede would have invented a fictitious pagan festival in order to account for a Christian one....Pagan goddess or clear and bright?
Compare Old English Ēastermōnað April, cognate with or formed similarly to Old Dutch ōstermānōth (in a translation from German), Old High German ōstarmānōd (Middle High German ōstermānōt, German Ostermonat , now archaic)...
A borrowing of the Old English word into West Slavonic (during the time of the Anglo-Saxon mission to Germany) perhaps underlies Polabian jostråi, Lower Sorbian jatšy, (regional) jastry , Kashubian jastrë, all in sense ‘Easter’; however, it has been argued that these are rather to be derived from a native base meaning ‘clear, bright’, and thus (via a connection with the coming of spring) show a parallel development to the Germanic word.