When I was really young, I used the handle "VGM10000", and today I have no idea what those initials stood for. A few people have posited "video game master", though, which is totally something my elementary school self would have thought was cool, so it was probably something along those lines.
As for PlayfulPhoenix, sometime in high school I decided I needed something that I actually liked, so I thought of new usernames for a while whenever I was bored - which was pretty often, actually. At this point in time, though, I no longer played competitively as I had done before, so I wanted a name that was interesting, but not imposing or obnoxious anything like that. I also wanted a name that was unique enough to always be available, while still clean enough to avoid the random upperCase lEttErs, numb3rs, and $ymbols that plague most names.
I can't recall the moment when I decided that a 'phoenix' was a good place to start, but I've always loved the concept of phoenixes in mythology and literature, as they're these imposing yet docile firebirds that, quite literally, are most striking at their lowest - when they die, in a burst of flame, and are then reborn from the ashes. Most monsters are just "really strong and scary and kill people" plus some unique feature - one eye, tail of snakes, whatever - but the phoenix is special because the nature of the creature's reincarnation symbolizes wisdom through continuous evolution. I may die today, but I'll be reborn a better version of myself tomorrow - and nothing can prevent me from doing so.
Phoenixes aren't bloodthirsty, arrogant, authoritarian or aggressive. They're impressive, but not menacing. Powerful, but not power-hungry. And they simultaneously symbolize the continuity and permanence and cyclical nature of our world, and represent the potential of people at their best: when they can dig deep in their failures and losses, and become better from them.
...Of course, "Phoenix" alone is a pretty generic name, so I added "Playful" to reinforce the "I'm in this to enjoy myself, not to get the highest KD ratio" angle. It also lends credence to the angle of a phoenix as a generally cooperative creature, and the name "PlayfulPhoenix" even rolls off the tongue pretty well IMO.
Anyways, in retrospect, I probably overthought my name just a tad, and most of the meaning I derive from it likely goes over the heads of everyone else. But I'm one to overthink things, and I really like the name. I'll probably use it for many years to come.