Best option: Quit your current job and start with a new employer using your valid documents.
Your employer is not law-abiding: Many employers knowingly and deliberately hired undocumented immigrants to pay them lower wages or help out individuals from their community or wanted to avoid paying Uncle Sam or some other reason. If you currently work for such an employer, your employer probably knows what is going on, and chances are that you might be able to easily transition from the invalid to valid number because the employer will simply input the new information (assuming s/he does not let you go because as a legal worker you will now demand fair wages and he maybe forced to pay Social Security and Medicare taxes to the IRS).
Your employer is law-abiding: If you used fake papers to find work, you simply cannot go to the Accounting department and simply ask for a Social Security Number change form (ha ha ha, no such form exists because these numbers cannot be changed). While a kind employer might simply fire you or ask you to leave employment immediately, some employers may actually notify law enforcement. Many companies will doubt your moral conduct for lying about your immigration status and may deal with it accordingly, most likely by asking you to resign. The right thing to do is to leave this work and find a new employer.