The majority of the Americas as a whole were colonised by Europeans, that doesn't mean you should call the entire two continents "European America".
"Latin" relates to a culture and language. "Iberian" relates to a physical region. If someone were to say something is "Latin" I would understand they mean that it is related to the Latin cultures. If someone were to say something is "Iberian" I would assume it comes from the Iberian peninsula.
The phrase 'Latin America' was coined by a French person, if I recall correctly. If you want to start saying "Iberian America" you can give it a shot, but I highly doubt it will catch on.