You need to establish your citizenship with Social Security if you haven't already.
Have you done so?
It should be in your records already.
Unfortunately, no relevant information is found.
I don't have any official U.S. documents, they were lost in a fire recently.
If that is the case, other documents may be deemed acceptable such as an officlal employee card.
What would those other documents be? What might Social Security ask about your immigration status?
social security will ask you for your child's current U.S. immigration document from DHS.
is it really necessary to tell the employer about a name change?
yes, it is. If you don't, it could lead to delays in your child's and your's tax refund.
And what if I'm a foreign worker?