Arisbe (Αρίσβη) can be:

• A daughter of Merops and a (pre-Hecuba) wife of Priam of Troy
• Another name for Batea, a person in Greek mythology
  
• In Homer's Iliad, a city in the Troad. It is mentioned three times. In Book II, where Asius is described leading Trojan troops from Arisbe and other Hellespontine cites; in Book VI, in which an account of the slaying of Axylus is given, who lived in 'well-built Arisbe'; and in Book XXI, in which Eëtion sends Lycaon to Arisbe after ransoming him.
  
• Charles S. Peirce's house, which he named Arisbe, inspired to do so by the account of Axylus, who welcomed all passers-by into his house in Arisbe.

Apollodorus:

But after that Ilium was captured by Hercules, as we have related a little before, Podarces, who was called Priam, came to the throne, and he married first Arisbe, daughter of Merops, by whom he had a son Aesacus, who married Asterope, daughter of Cebren, and when she died he mourned for her and was turned into a bird. But Priam handed over Arisbe to Hyrtacus and married a second wife Hecuba, daughter of Dymas, or, as some say, of Cisseus, or, as others say, of the river Sangarius and Metope.

Greek Mythology