Howdy.
I chose my name, which will become my legal name, to be “Jimmy Thomas Kirkbride”. My original legal name was chosen for me, and inherited from my family, and I don’t see myself as part of that clan any longer. Thus, by choosing my own name, I am expressing self-mastery (or at least self-ownership). I am pleased that my family and long-time friends call me by my given name, as it exemplifies the divide between us (that is, who I am, and who I was; the same person they still see me as). It would be far more difficult to grow on my own terms if the people who know me so intimately (and simply for so long), and who also have the ability to hurt me in ways unfamiliar and inaccessible to most anyone else also tried to relate to me in the context of the life path / direction I have chosen, through the use of my name of preference. Simply put, the use of that name by people I don’t necessarily like or trust sullies it, and they have no right to speak it.
At the other end of the spectrum, my handle “Tiberius James” is simply that. It is an online tag with no inherent magical or mundane significance, save that I think it’s kinda neat, and the etymological significance for which it was chosen represents a great deal of what I believe.
As I am currently working through the Abyss, and (hopefull) soon will be entering the Golden Dawn grade of Magister Templi (alhough I would like to make it clear that I am not a member of the GD or any other magical order). With that grade comes the adoption of a new name, but one which is provided by providence, rather than any particular spirit or via being consciously chosen by myself. That will be my true magical name, and represents who I am (on a magical level) and who I will be, during this period of my development. I’m afraid I most likely won’t be sharing it. If I do, however, it will be on account of my having developed (or encountered) a sigilised form of the name which I definitely won’t be sharing, and which trumps the name in terms of their both being unique identifiers (magically speaking, of course), as a sigil is even more specific than even a full name.
So, in answer to your question… Names are both simply labels used for identification, and at the same time, the entire, encapsulated sum of all that the name represents. To this end, the adoption of several names for different purposes (of which, magic may be just one purpose, or a particular kind of magic as distinct from the rest of one’s practise) makes perfect sense, and would likely aid in compartmentalising the various dynamic aspects of one’s self that seem to be part-and-parcel of a magical life (and which the vast majority of the mundane world will not have, as they struggle with their unrelenting disappointment over just the one persona they permit themselves!)…
Naturally, the inclination to change, modify, discard and invent new names at will (albeit according to their existing a worthwhile, symbolic reason for doing so) also makes perfect sense, and is the logical continuation of one’s deciding to adopt multiple names, in the first place:)
Kind regards, Tj.