Rogue is a name that does a lot of work in a single syllable: it signals that the animal has a complicated relationship with authority, that the owner has affection for that quality, and that there's probably an X-Men reference somewhere nearby. It's a name chosen by people who find rule-breaking charming rather than problematic.
The X-Men Connection
Rogue — the Marvel Comics mutant who can absorb others' memories and powers through touch — is one of the most compelling characters in the X-Men universe precisely because her power is also her curse. She can't be touched without consequence. Naming a dog Rogue after her is either a statement about the animal's untouchable quality or an appreciation for the character's combination of power and vulnerability. Female dogs with strong, independent personalities attract this name most frequently.
The Literal Reading
A rogue animal is one that has separated from the herd and operates independently — a reading that fits cats especially well, and dogs with high prey drive or selective obedience. Huskies, Belgian Malinois, and escape-artist mixed breeds all seem to collect this name as a candid acknowledgment of the animal's operating style.
Sound and Contrast
Rogue is one syllable with a soft R opening and a wide-open vowel, which gives it more acoustic warmth than its meaning suggests. The contrast between the gentle sound and the independent connotation is part of the name's appeal. Compare Bandit and Rebel for names in the same outlaw-energy register.