The Goddess, in her form Amaterasu is the spirit of the first principle.
The Sun, the center of our solar system, symbolizes the central place of the Goddess in existence. The planets which revolve around Her are dwarfed by comparison. By acknowledging the central place of the Goddess in our lives we pass from the dark night of the patriarchy to the dawn of the Goddess. She dawns in her heart when we accept her principles. This illuminates our spirits and enables us to live in balance once more.
Ideally the ritual of acknowledgement of the Goddess should be performed in the company of others who have done so previously. There is no reason it cannot be done alone. After doing so, an informal celebration can occur. There is no particular ritual required other than the three-fold recitation of the first principle, and no documentation need be created.
When performing the ritual of the acknowledgement of the Goddess, you should select a Goddess name to use in the circle of the Goddess; this is typically a name of a historical Goddess, or a female name associated with a Goddess in some way. Both women and men do so. There is no need to disclose this name to those not on the path of the Goddess, or actually change you legal name. The Goddess name is not particularly secret. You can change this name if you want at any time. It is just a mental exercise to remind you that the Goddess is in you as in all.
The mantra of Amaterasu (time of day: dawn): "Blessed Amaterasu, lead me into your light from the shadows. I walk in beauty. I walk in peace. I walk in balance on the path of the Goddess. Blessed be."