Do I need to provide you with a
photo ID to legalize documents
at a U.S foreign embassy?
Yes and no.
99% of the time U.S foreign embassies and consulates in Washington D.C do not require you to provide them with any sort of photo identification.
But for a few countries like the China Embassy will require you to submit photocopies of your passport (top and bottom panels) along with your documents. The Chinese Embassy also requires a document legalization application form to be filled out by you that can be downloaded and completed here.