Rodgers is a patronymic surname deriving from the given name of "Rodger" commonly used by the Normans and meaning "son of Rodger". Variant form of Rogers. The name Rodger is of Old German origin and is likely derived from the Germanic name Hrodger meaning "famous spear", composed of the elements hruod "fame" and ger "spear". In England, the name Rodger could’ve derived from the pre-7th century Old English name Hrothgar, which means 'fame spear' ("hroð" fame or renown, "gari" spear), the first reference to which is in Beowulf, the Anglo-Saxon epic poem.
https://en.wikipedia.org/wiki/Rodgers