It's kind of a long and personal story, so please bear with me for a moment.
You're free to skip this if you're not interested.

First and foremost, I didn't like the name "Blaui".
Other people liked it, which I think is cool! But I didn't. It's a name I thought of when I was 9 years old, and since I grew up with the German language, the name really just boils down to "blue but in German and it has an i at the end to make it sound cuter".
I even started using my real name in some places because of it, but it felt really weird when people I barely knew called me by it.

Additionally, though ironically not as major, I associate that name with some unpleasant memories. I used to be an asshole (I'm not a perfect person, shocking, I know), and I'd rather have that part of my past not be associated with the person I am now.

Within those 15 years of sticking to Blaui, the name underwent several variations throughout, such as originally using Blaui-Supi (with "Supi" kind of translating to "super but cute") for Habbo Hotel as my first website (remember that thing?).
I had actually made another account on it prior, but (un)fortunately I don't remember its name anymore.
I do remember somehow convincing my sister to use a similar name for her online adventures, though.

After that, I had a clan tag attached to my name (for a very short period in time, I was even known as simply "Kirby"), and I eventually settled on Blaui, with PuffballBlaui as an extended name for when I can't use Blaui. You can take a guess why.
I've used that naming scheme for a good 5 or 6 years until, finally, I arrived at BlizzBlu.

As you can probably tell, I didn't entirely ditch the theme of my name. The "Blu" part of "BlizzBlu" was meant to reflect that, and as I was brainstorming some names when I thought of changing it, BlizzBlu instantly stuck out as my personal favorite.

So here we are now! Hope you enjoyed that history lesson.