Craft names are a relatively recent innovation, in the occult world it seems, and are symbolic of the initiates rebirth into the craft. The craft name is chosen by the prospective initiate after much thought and meditation, and conferred upon them at their self dedication or initiation. It's purpose is not to conceal their true identity, but to reveal it.
As for choosing a magical name, this is where most of the difficulty occurs. There is no one right way to arrive at your craft name. It may be taken from the names of deities, crystals, herbs, animals, trees, virtues, mythic heroes, common names in other languages, magical goals.... The possibilities are virtually without limit. The name may be anything that you feel is representative of your inner spirit, your magical goals, your deepest dreams. It should be something that you feel attuned with. Generally, when the correct name is found you will feel an instant attraction to it and simply know that it is right. It is possible as well that this name may be correct at this time, but that at some future point in your development you will find that a different name calls to you.
Unlike given names, magical names can evolve and change with the person they belong to. So the name you choose today may or may not be your name for life, it will depend upon where your path leads you.
It is also possible to never choose or use a magical name. It depends upon your tradition how much emphasis is placed upon having one. If you are solitary and do not feel the need for one, then don't force yourself into it. If at some future point your feelings change you can always select a name at that time
These can be sources of name inspiration. Even other's craft names can inspire you in your choice, perhaps part of someone else's name strikes you as particularly 'you'. This can be a jumping off point for arriving at a name of your own. Books can also be good sources. Works of fiction, collections of myths, and other writing may contain just what you are looking for. It generally works best to simply keep an open mind rather than searching strenuously. The name will come when the time is right, you can't force it. (Spiritual.com.au)