I know exactly how you feel cause i did the exact same thing - changed my name and family still doesn't know. It's well worth it in every other aspect ( but I still fear they'll find out some day, some way).
There are a number of scenarios where they might find out about it: if the name is on your mailbox...if your parents need a copy of your birth certificate for some reason (don't know what such reasons would be in the U.S.), if you're a student, they might need a copy of your student's ID for their taxes....if there's a family insurance plan.....an inheritance matter...if money is sent to you etc.