Named after the Classical name for modern Po River in Italy.
Padus Vallis is a valley in the Memnonia quadrangle on Mars that empties into the Medusa Fossae Formation. Padus Vallis is one of many valleys that empty into the Medusae Fossae Formation. (wikipedia entry)
A vallis is a valley. On Mars large valles are named after words for Mars/star in various languages. Small valles are named after classical or modern names of rivers.