No, it's related to domingo, which means Sunday in Spanish, because it was discovered on Sunday. Compare Dominica, another independent country.
Thank you, had thar doubt all day!
Yes, according to Dr. Albert Batista as quoted in [this story] (http://hoy.com.do/explican-origen-del-nombre-de-la-republica-dominicana/) in a Dominican newspaper. Here's the key paragraph (my translation):
"Dr. Albert Batista, on behalf of the Standing Committee Ephemeris Patrias (CPEP), attributed the Dominican Republic name to a recognition of the Religious Order of the Dominicans for their contribution to the defense of human rights of indigenous and development of education and Legal Culture in the country, since the arrival of Europeans."
"She explained that the order of the Dominicans contributed to introduce the First Letters to the formal establishment of the first University of the continent in 1538, today the University of Santo Domingo (UASD)."
"She noted that Duarte* and los Trinitarios** catalyzed what was the historical process and use the name Dominicana to recognize the Dominican Order."
** [Los Trinitarios] (http://en.wikipedia.org/wiki/La_Trinitaria_(Dominican_Republic)), secret society founded by Duarte to fight for Dominican independence from Haiti.