A pseudonym is an identity.
It may not be the identity with which the pseudonymous person was born, but it's an identity nevertheless. Far more excellent writers than I write online under pseudonyms, building up reputations around those not-given-at-birth names that are every bit as valid as whatever praise or contempt I've earned under my given-at-birth one.
Furthermore, there are some excellent reasons (see under "Bosses, not with it" and "Stalkers, online and otherwise" and "Crackpots, fielding endless e-mails from") that given-at-birth identities can be risky online, and potentially disproportionately risky for women. Which is to say, disproportionately risky for, um, half of everyone everywhere.
Which is why it's frankly rather silly and shortsighted of Google+, the hot new social network of the moment, to be closing accounts registered under pseudonyms. I mean, I understand that the big G would consider identities associated with, e.g., actual credit card accounts and consumer behaviors, to be strongly preferable. But if I were building a social network, I think I'd probably want Scicurious in it, because even if I can't get useful consumer behavior data out of her pseudonymous profile, I'll bet there are people who would join a not-quite-baked social network if it meant yet another opportunity to watch the fun when Sci puts on her ranty pants.
Which is to say, if you're trying to get people to join a club, you really don't want to kick out all the cool kids.
So, hey, there's a petition you could sign, if you think maybe Google should know they're being a mite dense about this whole thing. It is, as they say, the least you can do.