Poe appears 65 times at rank 1598 on male pets. The name is almost certainly a literary reference to Edgar Allan Poe, America's most iconic dark-romantic writer, though the Star Wars connection (Poe Dameron, the X-wing pilot) provides a second pipeline that became relevant after 2015.
The Edgar Allan Poe Pipeline
Edgar Allan Poe wrote The Raven, The Tell-Tale Heart, and The Fall of the House of Usher: a body of work deeply associated with ravens, death, and gothic atmospherics. A black cat named Poe is almost a requirement for owners with gothic or literary sensibilities. The name belongs alongside Edgar and Raven in the gothic-literary pet name set. The human comparison is at /names/poe.
The Star Wars Layer
Poe Dameron, the best pilot in the resistance played by Oscar Isaac, gave the name a second, brighter cultural register after The Force Awakens in 2015. A dog named Poe could be citing either reference, and the two don't conflict. Border Collies and Belgian Malinois fit the capable-pilot reading.
The Counter-Reading
Poe is a one-syllable name with outsized cultural weight. It works best when the dog or cat has a personality that justifies the reference: brooding, intense, or startlingly capable. A golden retriever named Poe is simply ironic.
