So I am connected to someone in Messenger and that person identifies by my real name. How does that happen. Seems like serious breach of security.
Check your profile... yahoo can't give out information you haven't given freely at some point. You may find it appropriate to use an IM tool like trillian that lets you have different profiles for different types of contacts (personal, work, very private) yet be online for all at the same time.
check your privacy settings, im sure there is an option on what to share and what not to share..but if you signedup with your real full name, it might show by default...like skype does