Title: People of the Dominican Republic
Content:  Historically the Dominican Republic was known as Santo Domingo, the name of its present capital and its patron saint, Saint Dominic. Hence the residents were called "Dominicanos" (Dominicans). The revolutionaries named their newly independent country "La República Dominicana". It was often referred to as the "Republic of San Domingo" in English language 19th century publications. The first recorded use of the word "Dominican" is found in a letter written by King Phillip IV of Spain in 1625 to the inhabitants of the Captaincy General of Santo Domingo. In this letter, which was written before the arrival of French settlers on the Western side of the island, the King congratulates the Dominicans for their heroic efforts in defending the territory from an attack by a Dutch fleet. This letter can be found today in the "Archivo General de Indias" in Seville, Spain. Another name that's been commonly used is "Quisqueyans". In the national anthem of the Dominican Republic the author uses the poetic term Quisqueyans instead of Dominicans. The word "Quisqueya" is a derivative from a native tongue of the Taino Indians which means, "Mother of the Lands." It is often used in songs as another name for the country.
Title: Dominican Republic
Content:  English until the early 20th century. The residents were called "Dominicans" (Dominicanos), the adjectival form of "Domingo", and as such, the revolutionaries named their newly independent country the "Dominican Republic" (la República Dominicana). In the national anthem of the Dominican Republic (himno nacional de la República Dominicana), the term "Dominicans" does not appear. The author of its lyrics, Emilio Prud'Homme, consistently uses the poetic term "Quisqueyans" (Quisqueyanos). The word "Quisqueya" derives from the Taíno language, and means "mother of the lands" (madre de las tierras). It is often used in songs as another name for the country. The name of the country in English is often shortened to "the D.R." (la R.D.), but this is rare in Spanish.
Title: Dominican Republic
Content:  The name Dominican originates from Santo Domingo de Guzmán (Saint Dominic), the patron saint of astronomers, and founder of the Dominican Order. The Dominican Order established a house of high studies on the colony of Santo Domingo that is now known as the Universidad Autónoma de Santo Domingo, the first University in the New World. They dedicated themselves to the education of the inhabitants of the island, and to the protection of the native Taíno people who were subjected to slavery. For most of its history, up until independence, the colony was known simply as Santo Domingo – the name of its present capital and patron saint, Saint Dominic – and continued to be commonly known as such 
Title: List of Dominican Republic Provinces by etymology
Content:  This article provides a collection of the etymologies of the names of the provinces of the Dominican Republic.
Title: Dominic
Content:  Dominic is a name common among Roman Catholics and other Latin-Romans as a male given name. Originally from the late Roman-Italic name "Dominicus", its translation means "Lordly", "Belonging to God" or "of the Master". Variations include: Dominicus (Latin rendition), Dominik, Dominick, Domenic, Domenico (Italian), Domanic, Dominiq, Domonic, Domingo (Spanish), Dominykas (Lithuanian), Domingos (Portuguese), Dominggus; and the feminine forms Dominica, Dominika, Domenica, Dominga, Domingas; as well as the unisex French origin Dominique. The most prominent Roman Catholic with the name, Saint Dominic, founded the Order of Preachers, also known as Dominican friars. Saint Dominic himself was named after Saint Dominic of Silos. Notable people named Dominic, Dominik or Dominick include:
Title: Saint Dominic
Content:  Saint Dominic is one of the few historical figures after whom two sovereign countries are named: Dominica and the Dominican Republic. The capital of the latter, Santo Domingo, also bears his name.
Title: Dominica
Content:  Dominica's name is locally pronounced with emphasis on the third syllable, following the Spanish pronunciation of its name given to it by Christopher Columbus.
Title: Rafael Trujillo
Content:  In 1936, at the suggestion of Mario Fermín Cabral, the Congress of the Dominican Republic voted overwhelmingly to change the name of the capital from Santo Domingo to Ciudad Trujillo. The province of San Cristóbal was renamed to "Trujillo" and the nation's highest peak, Pico Duarte, to Pico Trujillo. Statues of "El Jefe" were mass-produced and erected across the Dominican Republic, and bridges and public buildings were named in his honor. The nation's newspapers had praise for Trujillo as part of the front page, and license plates included slogans such as "¡Viva Trujillo!" and "Año Del Benefactor De La Patria" (Year of the Benefactor of the Nation). An 
Title: List of country-name etymologies
Content: "Republic of Santo Domingo", the capital city of the Spanish-held region of Hispaniola since its incorporation by Bartholomew Columbus on 5 August 1498 as La Nueva Isabela, Santo Domingo del Puerto de la Isla de la Española ("New Isabela, Saint Dominic of the Port of Hispaniola") either in honor of Sunday (see Dominica above), his father Domenego, or Saint Dominic's feast day on 4 August. Nicolás de Ovando shortened the name to Santo Domingo de Guzmán upon the city's refounding at a new site after a major hurricane in 1502. Dominic himself was named for Saint Dominic of Silos, the monk at whose shrine his mother was said to have prayed. Dominic (from the Latin Dominicus, "lordly" or "belonging to the Lord") was a common name for children born on Sunday 
Title: Saint-Domingue
Content:  of a slave rebellion breaking out in their own region. Today, the former Spanish possession contemporary with the early period of the French colony corresponds mostly with the Dominican Republic, whose capital is Santo Domingo. The name of Saint-Domingue was changed to Hayti (Haïti) when Jean-Jacques Dessalines declared the independence of all Hispaniola from the French in 1804. Like the name Haiti itself, Saint-Domingue may refer to all of Hispaniola, or the western part in the French colonial period, while the Spanish version Hispaniola or Santo Domingo is often used to refer to the Spanish colonial period or the Dominican nation.

Question: how did the dominican republic get its name?
Answer: patron saint, Saint Dominic.