The name Penelope means bird this is one of the reasons why she is called Avisa.
In the book Willobie His Avisa , Avisa is constantly referred to as an eagle .
The name Penelope is classically linked to an eagle because in the Odyssey Penelope had a dream of a huge eagle that savaged a flock of Geese . This was supposed to be a portent warning of Ulysses return and his eventual slaying of Penelope's suitors. But Willobie his Avisa is a book of opposites and the author is reversing the legend, in this context it is PENELOPE WHO IS THE EAGLE and it is Penelope who has a destructive effect on her suitors.
This particular dream was specifically mentioned in Willobie His Avisa's follow up libel " Penelope's Complaint" The constant comparison of Avisa to an Eagle is the author's way of intimating that Avisa's real name is Penelope..