As an example, most of the photos I use as avatars, etc. I took myself with the ten-second timer on the camera. And that's not only selecting a location, and posing, but choosing, cropping and tweaking the picture - to attempt to create a look. I still do it to amuse, and as a form of self-expression, but they also remain masks to hide behind.
The issue has arisen not in the world of visual images, however, but in the written word. I have made web-sites, written blogs, done online interviews, etc over the last decade, and they form a loose autobiographical project in themselves. Indeed, a journalist/Star Wars fan spent some time digging through that online material to compile a portrait to post on Wookipedia. That material has since migrated to Wikipedia, and although it amuses me I don't feel the right to edit the stuff (that really does smack of vanity). So it contains some errors, or misleading details, which I would attempt correct in my own version.
The issue of an objective portrait has arisen because someone has suggested writing a biography of me, involving plenty of research - interviewing old friends, co-workers, ex-lovers and all that, as well as extended interviews with me. Do I want to see myself as others see me? Relinquish control of the final image? I never think of myself as sufficiently interesting to appeal to a professional publisher - but if someone else sees a market, and can exploit it, then perhaps that adventure would prove amusing in itself.
So, a portrait, or a self-portrait? I don't quite know how to decide.