Leto I (the first) was Paul's father, the
Duke of
Caladan, until being forced into taking up the
fief of Arrakis by Padishah Emperor
Shaddam IV.
It was Leto II, Paul's son, that became the God Emperor of Dune for about 3500 years after accepting the sandtrout skin, slowly metamorphosing him into a sandworm. The populace rather looked upon him sort of like they would Shai-Hulud (the Fremen word for a sandworm deified). He also led humanity upon his Golden Path.