And all these years I thought the country was Santo Domingo.
Well, it is.
The problem with the DR is that officially the country is known by the name of its government and not by the name of the country.
In Cuba they don't have this problem because the name of the country is Cuba, which also happens to be the name of the island, but the name of the government is Rep?blica de Cuba which also translate to Rep?blica Cubana (Cuban Republic).
In Mexico they also don't have this problem, because the country is called by its name (Mexico), but its government is Estados Unidos Mexicanos or something like that (United Mexican States).
Haiti herself doesn't have this problem, because people do call the country by its name (Haiti), but its government is called Republique D'Haiti (Rep?blica de Hait?) which is also translated to Republique Haitienne (Rep?blica Haitiana or Haitian Republic).
Then there's DR complicating something that is quite simple and straight forward. The name of the country is Santo Domingo, ehich outside Spanish-speakers is hardly used anymore (Americans used to call the country by its name until some time in the 20th century when it went 'out of style'). The name of the government is Rep?blica Dominicana (Dominican Republic) which also translates to Rep?blica de Santo Domingo (Republic of Santo Domingo).
Many people are oblivious that the term Dominicans derives from the Domingo after the Santo.
So, technically, those calling the DR "The Dominican" should really say Santo Domingo. Those very same people that say "The Dominican" would never say "The Cuban" for Cuba or "The Haitian" for Haiti or "The French" for France or even "The Canadian" for Canada. It sounds wrong because it is, but with "The Dominican" is a wrong thing that through repetition many people have joined the bandwagon of sorts.
I personally like Santo Domingo better. If rolls smoothly from the tongue, especially compared to Dominican Republic which in any language requires quite some effort to pronounce. Its also way too formal and way too long for such a small country.