The entire ancient evidence for the goddess behind the name is a single sentence, and it is short enough to give in full.
Bede, in De Temporum Ratione in 725, explaining the old English month names, writes that Eosturmonath has a name now translated as the paschal month, and was once called after a goddess of theirs named Eostre, in whose honour feasts were celebrated in that month. He also names Hretha for the month before, and says nothing further about her either.
That is all. Bede gives no description of the festival, no rites, no attributes, no myth, no animal, no egg, no hare.
Whether the goddess existed was disputed for a long period, with some scholars holding that Bede inferred her from the month name, a reasonable suspicion, since he was reconstructing pre-Christian material at a remove. The position shifted in 1958 with the discovery near Morken-Harff in Germany of over a hundred and fifty Romano-Germanic votive inscriptions to the matronae Austriahenae, whose name shares the root. The inscriptions do not name Bede's goddess, but they establish that divine names of that formation existed in Germanic-speaking areas, which makes invention much less likely. Most specialists now accept Bede was reporting a real tradition. Philip Shaw has argued she was local, a goddess of a specific Kentish or regional group, rather than pan-Germanic.
The hare and the eggs are attached to her by no source at all. The Easter hare is first attested in German writing in the seventeenth century; the connection to a goddess is Grimm's conjecture and later embroidery on it.