Final answer:
Alexhelios and Cleoselene, the moons of asteroid 216 Kleopatra, were likely named following the tradition of using Greek and Roman mythology for celestial bodies, possibly because, like Phobos and Deimos, they were captured asteroids that reflected the mythological narratives associated with their primary asteroid's namesake.
Step-by-step explanation:
The moons of asteroid 216 Kleopatra, Alexhelios and Cleoselene, were likely named within the tradition of using names from Greek and Roman mythology for celestial bodies. Considering that the moons of Mars, Phobos and Deimos, are probably captured asteroids and display irregular shapes that resemble those of smaller asteroids, it is plausible that Alexhelios and Cleoselene were similarly captured.
Textual evidence suggests that these moons were named after historical mythological figures related to their primary celestial body's namesake, in this case, the Egyptian queen Cleopatra, who was of Greek descent and had relationships with Julius Caesar and Mark Antony of Rome. The choice reflects the ongoing convention of using mythological names to label planetary bodies and their satellites, as highlighted by the precedence set by astronomer William Herschel and others.
Our knowledge of these celestial naming conventions stems from a variety of historical sources including the mythology-related constellations, the insights of Aristotle, and the practices of astronomers through history. For instance, the naming of features on Mars and other planetary bodies adhere to a set pattern that largely draws from these ancient mythologies.