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Have you legally change your name?
I did change my name.
then you should first inform Social Security.
where can I apply for a work authorization?
You can go to either the Department of Homeland Security DHS , U.S or the Citizenship and Immigration Services USCIS
for F-1 students currently working in curricular practical training what else is needed?
in that case, the Form I-20 must be provided together with the employment page completed and signed by your school official.
In case I need to give you as an evidence of a legal name change, can I use my old document, with my previous name?
yes, that would work if you changed your name more than two years ago, four if you are under 18, and your ID is not enough to identify you in our records.
What can I do if DHS did not authorize me to work?