Yes, very much to do with "east". It comes from the Old English word "eastre" and the Middle English word "estre", both of which mean "east".

As to how the name got associated with the festival we know as Easter, I believe it may be another example of the Christian church taking pre-existing pagan festivals and grafting Christian ones onto the same date as they converted native populations. Apparently, there was a pagan festival celebrated in April in honour of Eastre, a goddess of light and Spring and I believe the early Christians just hijacked this and used the pre-existing date as a new festival to commemorate Christ's death and resurrection.

helpfulndm20 | Rank: Student (44)
15 minutes after the question was opened (03/28/2006 08:46am)
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Originally, easter eggs were painted or dyed chicken's eggs and this is because they, along with rabbits, have been seen as fertility symbols for many many years. The Seder service at Passover uses a hard-boiled egg flavoured with salt water, and the tradition of fertility symbols has carried over to the Christian faith.

The idea of the egg-laying rabbit was introduced in America in the 18th century by German immigrants in the Pennsylvania Dutch area told their children that if they were good they would receive the eggs of the "Osterhase" or Easter Bunny.

helpfulcairina.moschata | Rank: Igor Sikorsky (2,081)
53 minutes after the question was opened (03/28/2006 09:24am)
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In ancient times the hare was the symbol of fertility in ancient Egypt but the rabbit has taken over that role in modern times. Also the hare and eggs have associations to the Anglo-Saxon spring goddess Eostre. Possibly, this is because both of them were also regarded to be emblems of fertility.
The fertility factor may hold the key in making rabbit more familiar as Easter symbol in America, as against the traditional hare. Rabbits beat hares by being more prolific.

The origins of the Easter Bunny aren't clear but the first recorded references to it are generally agreed to have come from Germany in the 1500s.

The German immigrants, who brought in most of the Teutonic Easter traditions here, made rabbits popular among the non-German kids. The German children used to have rabbit's nests filled with decorated eggs. They also used to build nests which looked so attractive that even the non-German kids demanded such gifts on the Easter. Why they ever thought that rabbits laid eggs is still a mystery to me!

The rabbit is equated with springtime and renewal of life, and the hare was also associated with the moon, whose cycles determine the precise date of Easter each year.

Over time these traditions presumably merged with the annual celebration of Easter itself, and now the Bunny is associated with Easter in much the same way that Santa Claus is the secular symbol of Christmas.