I watched a video on Youtube, not sure about the title nor how I got to it, but basically it says this:
Basically your name is not something you learn, it just comes to your mind as if you're brainstorming about things you can relate yourself to. There are also some strategies people use to choose one name instead of another. For example by calculating the number of destiny, which is the sum of the sum of all the numbers for your birth date, you can then brainstorm about that number. You can do the same thing putting numbers instead of letters following alphabetical order (A=1, B=2 and so on). Numerology aside, your best choice will be the one that most fits you.
Finally I have an advice. Everything is transient, and our thoughts are not an exception. Find a steady ground to work on your name, avoid things like tastes in music or movies. I haven't chosen a name for myself yet, I guess I'll use something that reflects the purpose I'm here for, but for now I use the nickname some friends gave me.
True magickal name actually isn't a term I've heard before, but many practitioners take on monikers to essentially protect their identity while practicing. This dates back to the Burning Times, when pagans were prosecuted for their beliefs, and the names were used as aliases so that nobody would be able to target them. Many people carry this on today as a way to remember the past, and what practitioners before us had to live through. Some don't feel the need, and some are given names; my magical name is Elidark (one word, not Eli Dark-- my, how gothic that would be), given me by my first teacher, who based it on a personal matter. There's no shame in naming yourself or going without one, just like there's no shame in being given one.