Final answer:
The term for the Romans' blending of Greek and local myths and rituals is 'syncretism', which involved cultural and religious adaptation, such as renaming Greek gods to fit Roman culture.
Step-by-step explanation:
The word that describes the way the Romans combined elements of Greek myths and rituals with local Italian myths, or with local myths in other areas of the Roman Empire, is syncretism. This process included adopting Greek aesthetic principles and mythological subjects in art, and incorporating elements from other cultures in religion.
For instance, the Romans reshaped the Greek pantheon to suit their culture, where Zeus became Jupiter, Aphrodite became Venus, and Hades became Pluto. Additionally, Roman religion was able to adapt to cultural changes, adding new gods and rites as they encountered different peoples throughout their conquests and actions like trading.