For your address change, what you need to update depends on what has gotten updated.
As for your shipping address, while it is stored with your account, you don’t need to update anything until you need to order something from Republic.
As for your billing address, if you updated your address with your bank, you should re-enter the credit card information so everything is up to date and matches what your bank has on file for you.
However, the most important place to update your address is the E911 settings. This is the address that Republic Wireless has on file for you in case your phone doesn’t have a cell signal but has a wifi signal when calling 911.
That is all the address information I can think of in My Account. You can double check the help section on how to update My Account.