FAA registration is a requirement for all people flying R/C model aircraft outdoor.
According with the AMA and FAA guidelines, members need to list both the AMA number and the Federal registration number on their aircraft. Also a basic knowledge of flight rules is required and achieved through a simple test. After you have registered you will have a registration number to put on your aircraft and after the TRUST test you will be able to print a certificate showing you passed. These are required by law of all recreational model aircraft used outdoors.
Here is a link to the FAA registration process through the AMA: https://amablog.modelaircraft.org/amagov/2021/05/11/update-to-faa-drone-zone-registration-and-renewal-process/ which provides detailed information on how to register to comply with the laws.
Your aircraft must be marked with your registration, here is a link explaining what to do: https://amablog.modelaircraft.org/amagov/2019/02/27/faa-registration-renewal-and-marking-your-aircraft/
You also need to have completed a basic airman test called TRUST: https://amablog.modelaircraft.org/amagov/2021/02/24/the-recreational-uas-safety-test-trust-faq/ which is a simple "open book" style test that you cannot fail.
And here is a link to take the TRUST test: https://www.modelaircraft.org/trust