Most people don’t know about it, but there is such a thing as common law name change. Works kind of like common law marriage. Plenty of case law to support it, too. She’d been called “Princess” for 20-30 years. Had it on all her checks, her DL, her passport, etc. Common law recognizes name changes without court sanction as a matter of right through free speech. Her name becoming Princess through usage was perfectly legal.
And frankly, if you had been there, you’d have seen there really was an element of racial biasing in the thinking of her detractors. She’s a good person, ran as an independent. Pro-life, pro-free market, etc. What do you want? Sometimes cultural bias affects even well-intended people. They think a name sounds funny or stupid because, well, that’s how it really sounds to them. So be it. But it was by no means illegal.
For example, you could call yourself “Sledge Hammer” for the next few years, and as long as you were “open and notorious” about it, and weren’t doing it fraudulently, i.e., to avoid other legal obligations (tax, child support, etc.), under Illinois statute, you can claim that name as legally your very own. Free speech. You can call yourself whatever you like.
Exceptions do apply. “0” for example, would not work. The courts that have looked at this don’t like numbers for names. But “Zero” probably would work.
The law is the whole law, not just the part you or I happen to be familiar with, and in reference to the whole law, she not only broke no law, she was asserting the rule of law. It was those denying her ballot access based on their lack of racial understanding who were at risk of breaking established constitutional law, which prohibits racial discrimination in the exercise of fundamental rights such as ballot access, even if it isn’t harmfully intended.
If she wanted to change her name legally more power to her, but on official documents you use your legal name, and trying to get her to do so isn't racist.