So you want to be a crime-related character?
Check out:
Alora SenShe is who you probably have heard of. She is not the ONLY crimeboss, but she's probably going to be one of the only ones to start with. Feel free to write stuff related to her into your BG.
Obviously, since your characters will all be pretty low level, it wouldn't make much sense to have been personally chosen by her to act as a low-level thug.
However! Feel free to include having seen her or even been a bouncer at one of her clubs when she entered or having been a lackey for her and got her drinks, etc.
She is a high-level boss and won't be making many appearances early on. But the background is there to include her Syndicate and hopefully can help get some cool ideas.
If you want nothing to do with her? That's fine, too. Just floating this out there for you all.
P.S. If you're a guard/investigator/smuggler/whatever. You can use her and her syndicate as points in your BGs, too!
