They dig through the rubble and ruins to find junk, artifacts, trash, and signage with the snazziest, jazziest labels and logos on them, that's how.
So here's some charts with random first and last names. Roll away, or mix and match to taste. Tweak the spellings as desired (and some are already altered below).
You can guarantee that my players in the upcoming Don't Mess With Wrexus campaign will encounter an Exxon Honda, a Jeep Supreme, a Manwich Snapple, a Reebok Bacardi, and a Quizno Pibb, whoever they happen to be.
(Special thanks to Idiocracy.)
UPDATE: The above lists have been expanded here.