You don't have to notify social security.
Depending on your state, you may need to notify the DMV. Some states require that you notify them of any change of address within 30 days of a move, and it's a criminal offense (although minor) if you don't do this. A few states don't care.
There is a form to notify the IRS of a change of address, but most folks just seem to wait until the next tax filing and show the new address with a "check" in the box stating that your address has changed.
Plans have a way of changing - but in the interim, just make sure you don't run foul of requirements to file US income tax and state income tax, plus FBAR if applicable.