There are at least two main types of risks that go along with internet anonymity in such virtual worlds. 

The first of these is the possibility of various types of cybercrime.  When people are on such networks anonymously or under assumed identities, they can easily put themselves in positions to commit crimes.   They can get other users to give them personal information that can be used for identity theft.  They might be trying to misrepresent themselves for the purposes of arranging sexual encounters.  This second problem is at least somewhat common with people pretending to be other than who they are to arrange for encounters with underage children.

The second major problem that can arise in anonymous virtual worlds is the problem of cyberbullying.  When people do not have to put their real names to anything, they are essentially free to say whatever they like.  They can do things like ruining the lives of young people who lack the emotional maturity to deal with hateful things being said about them, even by anonymous people.  There have been instances of youths committing suicide because of such bullying.

It is for reasons like these that many people advocate an end to internet anonymity.