The early church, and many Christians still today, called the day of Christ's resurrection Pascha. This is a Greek form of the Hebrew word for passover. If you know your new testament, you'll recall that Jesus' death (and resurrection) happened during the Jewish feast of Passover, and the Christian holiday simply kept the same name, as Jesus' death was supposed (according to the early church) to have been the ultimate Passover sacrifice.

When Christianity came to England, this festival replaced (according to Bede, who may or may not be a reliable source, since he had an axe to grind about how Easter should be celebrated) an older pagan celebration honoring the godess Eostre. Perhaps this holiday was stolen by Christians to one-up / replace the older celebration. Bede includes in his history of England (a different text from the one in which he talks about Eostre) a letter from Gregory the Great (the late 6th century pope) instructing Augustine, his missionary to Kent (S.E. England), to borrow the names of local holidays, along with local holy places, in order to make Christianity more palatable to the people he was trying to convert; it's possible that Easter was renamed (in English) as part of this program.

Or perhaps it simply became blended with a northern European holiday, in much the same way that many different cultural traditions have become mixed together during the modern Christmas season.

Both German and English call the Christian holiday Easter / Ostern, presumably after this older (entirely forgotten, but for the mention in Bede) holiday. In French, it's still named after Pascha (modern French: Pâques).

The connection with Ishtar is a false etymology. Ishtar was a middle eastern goddess, and her name sounds a lot like 'Easter', but 'Easter' is the northern European name for the holiday. In the middle east, when the holiday was being invented, it was named pascha after the Jewish Passover.