I think the “Imperial” marque was born out of the Chrysler - Packard merger.
Chrysler and Packard never merged. Packard merged with Studebaker in the late 1950s. Packards were produced for another year or two after that (actually, they were rebadged Studebakers) before the nameplate disappeared. There was a plan for a 4 way merger between Studebaker, Packard, Nash, and Hudson, but it never materialized. Nash and Hudson then merged to form American Motors.
The Imperial was a Chrysler-badged model from 1926 to 1955. In 1956 is was made its own line (like Plymouth or Dodge under Chrylser). Packard merged with Studebaker in the mid 1950s, and, as far as I know, was never owned by Chrysler.