Craft names, sometimes called magical or secret names, can be taken for a number of reasons...
A naming ceremony can be a symbol of birth. So if you dedicate yourself, or are initiated into a coven, a craft naming may be done to symbolize the birth of the new you. Initiations usually have a death and rebirth aspect to them, so the naming adds to that.
A magical name can also help you get into the right frame of mind for magic/worship. It will take on a special meaning for you as you begin to associate with those acts. It's like a pre-ritual purification rite, or putting on magical garb... all helps you to slip into the right frame of mind.
Some use a craft name as a way to hide themselves, if they are worried about losing their job or getting in trouble with family. It's an alias of sorts.
Some traditions - such as Egyptian traditions - believe that names have immense power. If you know someone's name, you have power over them and can control them. So you give yourself/find your secret name, your true name, so only that name holds power over you. This sort of name is never told to anyone, only the Gods know it.
Some take on a totally secret name, some have a name they use within their coven and no where else (and sometimes this is the secret name - to really show the bond of trust you must have with those in your coven), and some have a public magical name - for forums and public gatherings.
Some never take a magical name. It's really up to you if you want to do it or not.
There are also many ways to choose a name. If you join a specific tradition a name may be given to you - sometimes the name is divined in a message from a Deity, sometimes the coven members choose something they feel fits you.
A Deity or spirit guide may give you your name, in meditation or through some other way.
You may choose your own name. You can choose something which you want to strive to become like ("Bear" if you want to become strong, "Raccoon" if maybe you need a little of the trickster in your life). Some name themselves after a family or personal totem, or an animal they are somehow associated with. A Scorpio might include the word scorpion in their name. Someone born under the Fire Tiger in Chinese Zodiac may include that.
Some pick the names of famous people they admire - magical or not. An architect may like Imhotep. Some take old family names, or traditional names from the culture they are drawn to.
Some pick the names of Deities... but it's always best to know the Deity first, some really do not like this! However, something like, SatBast - Daughter of Bast - might be a fine choice.
Some use a lot of numerology in finding their names, but I don't know much about that myself.
If you decide to pick your own name, there's no rush. Take a long time to really think it through. Maybe you want to include it in a dedication ceremony, and it can take a year or years to get to that point. It can also be good to take originality into consideration if you pick a name for yourself... You want your name to be yours. There are a lot of Ravens, Moons, Willows, and Merlins out there. There's nothing wrong with such names (hell, I'll be the first to admit that my secret name is a bit cliche!), but it's something to consider.
There are actually three different types of magickal names you can take, they're not all the same thing. First, is the Craft name, the one that you go by in the Craft. This is what other Witch's and pagans will call you at public/open gatherings. As Alexandria stated, this is usually chosen by the practitioner. Second, is the Workiing name, the one that you go by in your private workings and only you and the Gods know it. Now, sometimes, as Alexandria said, this name is chosen by the practitioner as well, or it is bestowed directly from the Gods themselves. Third, is the Coven name, the name that you are known by if you practice in a coven setting. Usually this name is bestowed by the coven elders.
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