Using Pseudonyms

I was reading some on bgblogging, and I found some things that relate to teaching with blogs.

She had a link to a blogger who suggested allowing and even requiring students to use pseudonym's on blogs because if they make a mistake it becomes a public mistake that could be there for a long time. I think we need to think about this. For the student's safety, I'm thinking Internet stalkers, etc., it would be a good idea to have pseudonym's. What would be the cons?

Will Richardson said this:

But on the high school level, there is no choice. I've mentioned that we only let our kids use first names, pseudonyms if they prefer, and that they refrain from even mentioning other students by full name. They'll have plenty of time after high school to lay claim to their public body of work. But I struggle with this
nonetheless. We want students to take ownership, we want them to be a part of
the larger conversation, yet how much ownership can they take when they write
anonymously? And when they know that the site will be "depublished" at the
end of the year? While it doesn't totally take away the value of the blog, it
certainly diminishes it.