If you're running a newer version of messenger it's possible that both you and the "other" will get the same messages. However, it will tell you the "computer name" of where the other "you" is signed in.
I'd recommend changing your password to something totally whacky, like my nick, or something.
Most times I've seen this happen though if from people who give away their password to a web service with a promise it will tell them who has them blocked. They consequently use your password/account and sent spam messages out about Acai berry juice or something stupid like that. A change of the password will fix it
It is possible, however, that you're signed into WM on a portable device like your phone though, so look into that....