if you get one letter,I would assume you can say it was a shipping mistake,it was not yours.
Happens sometimes someone uses a fake name ,happens to be your name.
I dont want to ask what kind of federal job,but if its "lower" level,mail man ect I think you will be fine.
if there is a polygraph involved then well I dont know.
All you can do is try and worst they can do is say no.