"Elwurd" is almost certainly not her real name. The revamped page mentions her "other aliases", and she says "call me Elwurd", not "my name is Elwurd". So what's her real name, and why is she hiding it? Trolls don't have a word for homosexuality, according to Karkat, and it would be kind of wasted if in-'verse she picked it for the sexuality reference rather than something plot-related. She also lies to others but reacts badly to being lied to, so she's hiding SOMETHING. "Liar" begins with L...

Her second name is literally Gay Girl, Elwurd is 100% a reference to the L word. That being said, the others imply she may buy and sell illegally, and there’s always the chance of her working with the rebels.