Latin America is called "Latin America" because the countries that comprise Latin America speak Spanish and Portuguese, which are descended from Latin.
Latin America is comprised of the countries, whose populations speak Romance languages: Spanish, Portugese and, to a lesser degree, French, which are all derived from Latin.
The French used "a common Latin origin" to justify their temporary occupation of Mexico. Napoleon III placed Maximilian Habsburg on the throne as Emperor of Mexico with the justification that both...