A letter concerning the book's publication gives two reasons for the author's chosen title. The first is the numerical connection, through gematria, between the book's name and his own name, Avraham Dov Ber.
The Holiness of the Land of Israel within the Book
The second reason relates to the holiness of the Land of Israel infused into his teachings and to the verse about God's eyes upon the land. The title Bat Ayin thus connects the author with the land for which he longed. The letter also concerns the transmission of the manuscripts and preparations for printing.
For further exploration: The Bat Ayin's Practices, Bat Ayin and Its Teachings andStories and Testimonies.