There are many methods for choosing a Craft name, the simplest of which is to take the name of your favorite character or deity from Pagan myths or legends, or the name of the animal totem, gem, or mineral that you seem to identify with.
A second method is to open to the index of a book on the mythology of your chosen tradition, Celtic, Norse, Mediterranean, or worldwide if you are eclectic, and then, using a pendulum, dowse the list of names of the mythological figures. Note which names caused the pendulum to respond, usually by changing the direction of its swing, and choose your favorite among these names.
An improvement on this method is to write the names selected by the pendulum on a piece of paper, fold it, and sleep with it under your pillow. When you awaken in the morning you will know your name to be.
Another method of choosing a Craft name is to cast the runes or draw a number of cards from a tarot deck. The number of cards or runes is determined by drawing one card or rune first and using its numerical equivalent as the number of letters to be selected. Then draw that number of cards or runes and lay them out in a row, from left to right. Each card has a number from Ace (one) to ten, Page, Knight, Queen and King are 11, 12, 13, and 14, respectively, and the Major Arcana cards are also numbered.
The number on each card tells which letter of the alphabet it represents; Ace = A, two = B, XXI = U, etc. Each rune has a phonetic value, so it is fairly easy to just read the name.
Any of these methods will be enhanced if they are performed within a Magick Circle. This would best be done during the Full or waxing Moon when magickal powers are strongest. When the Circle has been cast you might state your purpose with words like:
Lord and Lady, guardian spirits of the
Four directions,
I have cast this Circle on this night
That I might be given a name,
A name by which I will be known
To the Gods, and those within the Sacred Circle.
From the time that you have chosen your
Craft name until the night of your Initiation when you
are given the name in the sight of the Gods, you will
learn to identify with it as the name of your other self
in the spirit world. For this reason this is a secret
Craft name, traditionally to be known only by coven
members, and used within the magick Circle. While most
Pagans and Wiccans/Witches have a secret Craft name, many
also have a public one which they use when interacting
with other Pagans in a public context, such as a Pagan
gathering. This name serves a dual purpose. It
simultaneously tells something of the individual's
tradition and magickal interests, while it also protects
the privacy of the individual by not revealing his secret
Craft name or his legal name by which he might be
harassed by those not friendly to our Pagan ways.