How to inform conference organizers about your legal name
Your situation isn't uncommon. In particular, many women prefer to use their birth name rather than their married name for reasons of continuity, etc. Some people need to use an alias for various security and/or political reasons. 

Just include a note explaining the situation as you have here. If you are asked, you might offer to provide a photocopy of the first page of your passport for verification. But only if asked.