I sign semi-legibly but get bored in the middle of my last name and make some kind of squiggle.
My first name is Julia. In…whatever grade it was that I learned to write in cursive, I would make a nice fat J, then add stripes, whiskers, and a head with pointy ears, so it looked like a cat sitting with its back to you.
After a few more years, I wanted to make my handwriting a little more distinctive, so I developed some funky-looking thing where I didn’t connect all of the letters and never finished loops. Some of those habits clung, so now my J ends in a spike and I can’t make my ignoring cat anymore.
Same here.
I have a sort of loopy thing that’s definitely mine, but it’s not really identifiable as any particular name.
I have a bold, magnificent signature. It has become a little more stylized than it was 35 years ago, but it’s still obviously the same person’s signature. You can read my name in it, though it isn’t a paragon of legibility. I changed the way I wrote one of the letters about 25 years ago, but I’ve done it the new way since then. I don’t know what you call it when you initial something but that’s been the same for about 30 years.
I have a signature that’s very distinctive but it’s not exactly legible. I came up with it when I was bored in physics class and wanted to make a signature that said, “I’m far too important to waste my time actually writing my name out”. 
I’ve gotten a lot of compliments on it and a lot of “is that Arabic?”. Because of its illegibility, sometimes I’ll have a legible signature underneath it if there’s no place to just print my name as well.
My mom used to bitch at it (though my actual penmanship is perfectly nice, so don’t worry, Ma!), but she saw the advantage when I had to sign 5 brazillion times on my car loan/purchase paperwork.
Mine is fairly legible up until about halfway through my last name, so it reads something like Kythereia of Mount Olymnaksdlsj. If I’m really tired it goes something like Kytherasdfop of Mouisdqwepls.
Oddly enough, I have really good cursive handwriting.
I have a signature that is relatively illegible for cheques, printed letters, and the like. (It looks like it says Cath hli, more or less.) If it’s something really important, I’ll pay a little bit more attention to it, so that it actually bears some resemblance to my actual name, but is still pretty hard to make out.
However, when handwriting letters, I usually write my name in my normal handwriting rather than signing it, because handwriting and signing my name seems a bit much. I might add a little flourish though.
If I’m required to, I write my name legibly. One of the court officers has requested that - I guess my usual scribble wasn’t sufficient for her. So now at work I get all but the last ‘-ger’ all pretty.
My signature, OTOH, is a blur of loops. I rarely write out my first name, just the initials of it in a weird way (“THAT’s supposed to be a J?”). My last name has the first three letters, then a scribble.
It drives my mom nuts. If she has me sign anything I clarify whether she wants me to sign my name, or does she want my signature.