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.
Do I nee to establihs my citizenship with you guys?
Yes, if you haven't already done so, you need to prove your US citizenship.
In case I change my name, do I have to inform my employer only?
You'd have to inform your employer and Social Security.
What documents can I use as proof of citizenship?
Only certain documents are accepted as proof of U.S. citizenship, like the US passport, Certificate of Naturalization, etc .
In case I change my name, can I use my previous ID as an identity document for the process of getting a corrected card?