One of the primary reasons these days for having a Craft name is that it is another tool for putting your mind into a ritual headspace where magic works. Many of us live each day in a world that denies the existence of magic or even of the presence of Divinity. So when we step into circle we use a variety of tools to help our minds reach the point where we KNOW that magic does work and we KNOW that Divinity is present there with us. Candles, incense, certain rituals, ritual dress, working in a darkened room are all ways to open up the channels in the mind to allow that to happen. Likewise we have a name that we use in the mundane world and which identify the person who lives in that world. Our magical name belongs to the magical being which comes forth in circle.
In addition, our mundane name is one that was given to us by our parents. We may love it, we may hate it. We may not feel it fits who we truly are. Our magical name, IMHO, should be chosen to reflect the heart of who we really are or who we wish to become. And given time it will be come the real us. That's why the old magical traditions claim that true names have power. In most cases people chose their magical name for themselves. But in some Traditions you are given a magical name by your HPS or HP when you are initiated.
There are any number of ways to find your magical name. Sometimes it can come to you in dreams such as when my husband dreamed of talking badgers for three nights running. Or you can use numerology or other methods of divination to find your Craft name. Meditating on finding your name is another way to come by it. That's where my current magical name came to me shortly before my 2nd Degree initiation.
However you come by what you think might be a good name don't start using it immediately. Take a few days to let it sink in. Look at yourself in the mirror. Does the name seem to fit you? Do you feel foolish calling yourself that? When you speak your new name does it resonate throughout your body and soul as being who you are? Only if it feels absolutely and completely right should you assume it is indeed your Craft name.
Something else to consider. Many people try to take the name of a God or Goddess as their magical name. When you do that you can also expect over time that you will also take on the aspects of that Deity. So be very sure you know as much as possible about that God or Goddess to be certain you really want to reflect those qualities and live up to the standards of that Deity.
And on a final note, our magical names don't always remain the same. As we grow and change our names may come to no longer fit who we are or our aspirations. So don't be surprised if the name you initially chose is no longer right for you. For example, my first magical name was Phoenix because I was being reborn out of the fires I had gone through into a new and magical me. However, by the time I reached my 2nd Degree I had outgrown that name. And that's when my current magical name came to me during a meditation.