The word Dominica is the Latin word for Sunday, that being the 1st or 7th day of the week. It is the Latin equivalent of the English Sunday as the words do not share the same etymology, and is the root of modern day Romance language's (Romanic/Latin/Neo-latin languages) word for Sunday. Examples from the six most spoken Romance languages today would be; Domenica - Italian, Domingo - Spanish & Portuguese, Dimanche - French, Duminică - Romanian & Diumenge - Catalan.
Dominica (the Commonwealth of Dominica)is the name of an island state in the Caribbean. It was sighted and named by Christopher Columbus on 3 November 1493. Named after the day on which it was sighted that being a Sunday. Columbus was born in the Republic of Genoa, and would have therefore spoken Latin, Ligurian (this being his native language) and possibly Italian, but never wrote in his native language but rather in Latin. This would explain why he chose to use the latin version, Dominica, and not the Italian "Domenica" or the Spanish "Domingo" (the language of his financial backers - the Spanish monarchy).