Similar to Easter bunny and eggs of pre-Christian fertility goddess during spring equinox. Traditions are very persistent, even when they lose their original meaning.
You might be surprised that this theory doesn't actually have any material support.
Our sole historical source for the supposed worship of a goddess named Eostre among the pre-Christian Anglo-Saxons is the Ven. Bede, an 8th century Anglo-Saxon monk and fairly prolific writer. Bede's work The Reckoning of Time is our source here, and what Bede tells us is incredibly little.
First, it's important to understand what Bede was writing about, namely the names of the Anglo-Saxon months. He had been talking about how the Romans named the months, and other matters of calendar nomenclature, and so he decides to speak about the Anglo-Saxon calendar. In doing so Bede attempts to explain the etymology behind the names of the months, and to the month of Eostermonath Bede says it is named after a goddess named Eostre that was at one time worshiped by the Anglo-Saxons before they had converted to Christianity. He adds to this only to say that, in his own time that because the whole significance of the month was taken up by the importance of the Paschal Feast that it had become common to speak of the Paschal season by the name of this month; thus calling the Paschal Feast "Eoster", modern English "Easter".
Just as important as what Bede does tell us, is what is entirely absent: any mention as to how the old Anglo-Saxons worshiped this goddess. We aren't even told that she was a fertility goddess, that can only be assumed because her month was a spring-time month (so, it's a fair assumption to make). But there's nothing about eggs, or hares/rabbits/bunnies.
Then there's the other issue, as noted, Bede is the only source. Not just written source, but any kind of source at all. We have nothing to corroborate it, nothing that was written earlier, or even later. All later writers (such as Jacob Grimm) are entirely dependent upon Bede. And we have no archeological evidence.
This is also true with the only other month that Bede says was named after an Anglo-Saxon deity, Hretha (the month in question being Hrethamonath). Again, Hretha is only attested in Bede, here in his Reckoning of Time.
There is a possible alternative hypothesis that Eostermonath isn't named for a goddess named Eostre, but is instead named for the direction of the rising sun, the Dawn-month (as there
is an etymological connection between Eoster[n] and East). It's the month where the sun is observed as rising earlier.
Not that I want to disrespect Bede, it does seem quite possible that in his attempts to explain the meaning behind the month names, he may have offered his best and educated guess. Or, it's possible he was correct and we simply are not privy to whatever information or sources that were available to Bede.
The origin of the Easter Bunny, if there is any pagan connection at all, is completely obscured to us. Though as we can trace the Easter Bunny back to the German Osterhase, which seems to have (at least its most recent) origins in the medieval Christian use of the hare as a symbol. The hare was a symbol of virginity (due to an ancient mistaken notion in the Classical period that hares were hermaphrodites and could reproduce parthenogenically. So the hare became associated with the Virgin Mary,
The hare was also used in medieval church architecture as part of Trinitarian symbols,
Again, there may be older pagan antecedents from which Christians appropriated use of the hare as a symbol, but evidence in support of that seems slim at best. I'm not suggesting it didn't happen at all, only that it gets overplayed today due to a lot of mass misinformation.
This is one of those examples of where a "everyone knows that..." piece of information is actually just a commonly repeated non-fact. Like when people say that everyone in Europe before Columbus thought the world was flat. Well, no, not only is there no evidence of that, the actual evidence we do have actually says something very different.
-CryptoLutheran