Easter is a celebration of new life, and can be symbolised in chickens popping out of eggs and newborn baby animals. There is no need to remove the name, for Christians it means Christ rising from the dead, and for non-Christians it is a celebration of Spring.
The Easter Bunny has nothing to do with the Christian religion, so hunting for eggs this mythical beast has dropped is a secular festival. Just as Father Christmas has nothing to do with the Christian festival of Christmas. (Technically St Nicholas might have started it, but I am not going there)
Christians may choose to add in these secular bits to make their celebrations even more fun for their children, but there is no religious aspect to it.
So whilst I will be in church at Easter (and indeed most weeks of the year) I am not bothered about renaming secular activities. In fact I would be quite happy to have the two separated, Spring Egg Hunts and Father Winter? 