Prior to 1977, unissued notes were held at each federal reserve bank and were issued by a local Assistant Federal Reserve Agent. I would guess that prior to 1977, most or all of the unissued notes bore the name of the particular federal reserve bank that held them. After 1977, Federal Reserve Notes are issued by a Federal Reserve Agent or an Assistant Federal Reserve Agent when they are shipped from the printing facility in Washington, D.C. or Fort Worth, Texas.
Since issuing a note is actually an intangible accounting process on the books of the federal reserve banks, why would it matter which bank's name is printed on a particular note? All issued Federal Reserve Notes are equally accepted by every federal reserve bank and the U.S. treasury regardless of which bank's name is on the note. As an economist might say, they are fungible. I believe that the only reason the identity of the individual federal reserve banks are still on the notes is because of a legacy statute from the original 1913 Federal Reserve Act as amended.
So does anybody know, does the Bureau of Engraving and Printing and the individual Federal Reserve Banks make a special effort to always match up the name on the new notes with the name of the bank to which they are shipped. The way I see it, as a practical matter, it does't make any difference.