Because Spanish speakers and people descended from Iberian countries refer to themselves as Latinos. Spanish (as well as french, Portuguese, Romanian, Italian, and all the many dialects within them) is descended from Latin. Latin being the Anglicization of Latino we call it Latin America.

I'd also like to add that Greece is associated with Greek, not Latin. Even after the Romans conquered Greece Greek continued to be the Lingua Franca there and the rest of the eastern empire.

Sorry this is not an answer (although I imagine it has to do with Latin-speakers - Spanish, Portuguese - being there), but is Latin associated with ancient Greece? Wouldn't that be Greek?