Have you legally changed your name?
I haven't
are you currently working?
Yes, i'm currently working.
In case you change your name, inform your employer.
I am already legal in the country and I want to request a work authorization, can you indicate the necessary documents?
You can apply for a work authorization either in the Department of Homeland Security DHS , U.S. or in  Citizenship and Immigration Services USCIS and request a Social Security card from the Social Security Administration.
and for F-1 students what documents are needed?
You'll need to show us the  I-20 Certificate of Eligibility for Nonimmigrant Student Status.
What I'm legally able to do if I still don't have permission to work.