You will be required to sign the certificate with your name exactly as it appears on the certificate. Do not use the abbreviated signature and sign your name exactly as it appears on your Certificate of Naturalization. Have a backup copy of your Certificate of Naturalization and store it in a secure place. You do have the authority to make backup copies of your certificate. Copying for falsifying or altering the photograph, falsifying information on the certificate are unlawful practices.
Make sure you keep the certificate in a secure place as your Certificate of Naturalization is all you have to prove your right to live and work in the US. It should only be carried and used when you have to legally prove your citizenship (at the border or when applying for a job). You can choose a bank safe deposit box as it is the best place for storing your certificate as it is the most secure and most fireproof.
You can apply for a passport as the next step even if you do not have plans to leave the country anytime soon. It is an alternate form of legal proof of American citizenship and only US citizens can get US passports. So by having a US passport you have an alternate means of legally proving your citizenship. A US passport is valid for ten years.
You have to report the change in your immigration status to the Social Security Administration so that the social security database can be updated showing you as a US citizen. This database is shared with all federal and many state agencies. When your social security records are updated, it will be much easier to apply for and receive all social security benefits entitled to you in the future. Should you need to replace your social security card, getting a new card will be comparatively easier now since you are a US citizen. And remember in some states, some disability benefits are only available to US citizens. By updating your status with the Social Security Administration, you will qualify to receive all disability, retirement, and social security benefits for which you qualify as a US citizen. You have to file Form SS-5 to report the change b going to your local SSA office..
The next important thing you need to do as soon as you become a citizen is register to vote. As a citizen you have the right to vote and participate in the election process. This is a privilege only US citizens get. When you register, you will be issued a voter registration card, which is further evidence of your citizenship status. Your name will be added to the voter registration list, which is used by many municipalities, counties, and the federal courts for jury selection.
There are other activities you can take advantage of as a US citizen. You can run for public office and also work for the federal government. It is time to cherish your citizenship and contribute to the country as a model citizen of the US.