To change your address on your ham radio license you must change it in two FCC databases:
Universal Licensing System (ULS) License Manager
Go to https://wireless2.fcc.gov/UlsEntry/licManager/login.jsp
Log in with your FCC Registration Number (FRN) and password
In "My Licenses" section, click on your call sign
On the far right, under the "Work on this License", click on Update (to change your Licensee Name and Mailing Address)
Answer the fee question (probably No to both)
Then enter your new Licensee Information
CORES (COmmission REgistration System)
Log in with your FCC Username (email) and password
A security code will be emailed to you for the next verification screen
From the menus, select:
Manage Existing FRNs > Manage FRNs > Update/View FRN
Enter your new address and submit