Original: The name Dattatreya can be divided into two words - "Datta" (meaning given) and "Atreya" referring to the sage Atri, his physical father).
Simplified: The word Datta means "Given", Datta is called so because the divine trinity have "given" themselves in the form of a son to the sage couple Atri and Anasuya. He is the son of Atri, hence the name "Atreya."