"This is the kind of behaviour that, in the end, promotes crime. It is exactly what we don't want. We want more security online. It's anonymity which facilitates cyber-bullying, the abuse of children," she said.
"I was genuinely shocked that a public official could say such a thing."
Culture minister Ed Vaizey has also backed Goodman and said that he wouldn't encourage people to put false identities on the internet.
Vaizey told the BBC: "The way of viewing this issue is that we should with Facebook to ensure people feel secure using those sites and that there is not a threat of identity theft."