Final answer:
Rodriguez's phrase "two names, two worlds" refers to the duality of his Hispanic heritage and his assimilated American identity, highlighting the cultural and personal dichotomy he experiences due to his bilingual and bicultural life.
Step-by-step explanation:
When Rodriguez refers to "two names, two worlds", he is highlighting the dichotomy between his private identity and his public identity. The two worlds his name represents are the intimate, familial, and cultural world of his Hispanic background on the one hand, and the formal, public, and assimilated world of American society on the other. Rodriguez feels his first name, in its Spanish pronunciation, connects him to his family and his Latin heritage, whereas his surname, when Anglicized, is associated with his outward identity in American society. This duality encapsulates the larger theme of cultural assimilation and bilingual identity.