Interestingly, Star Trek: Federation states that North, Central and South America were unified into the American Empire at the onset of the Eugenics Wars.
No, actually, it doesn't. Nowhere in that book is the phrase "American Empire" ever used.
The book does make heavy use of the term 'Optimum Movement'. Is this what you were referring to? (And, IIRC, the Optimum was not an American grouping. Optimum took over many countries worldwide, not simply the US.)