As the Internet becomes the place for all kinds of transactions, from buying shoes to overthrowing despots, an increasingly vital debate is emerging over how people represent and reveal themselves on the Web sites they visit. One side envisions a system in which you use a sort of digital passport, bearing your real name and issued by a company like Facebook, to travel across the Internet. Another side believes in the right to don different hats — and sometimes masks — so you can consume and express what you want, without fear of offline repercussions.