If I was starting my career now, not like... fifteen years ago, I would go anonymous, work under an alias and be a pure webcomics person.
BUT because of when and how I started out, back in the mid-late 00s, in print stuff, leaning on being one of the few illustrators in a rural area and doing a lot of workshops in schools and libraries and the like, it's kind of out there now, because I work under my own name and I've appeared at plenty of events. It's not ideal for somebody with dismorphia issues, but it's what I've got. 
So you'll usually see me going under "Kate Holden" on my work, and when I draw myself, it's a fairly accurate approximation of what I actually look like, just heavilly simplified: