Massachusetts Republican Party
The Massachusetts Republican Party was founded in 1854. Drawing together abolitionist and nativist anti-Catholic elements, it quickly became the dominant political force in the state and a powerful arm of the national Republican Party. Significant founding figures include Senator Charles Sumner, formerly of the Free Soil Party, and Speaker of the House Nathaniel Prentiss Banks, formerly of the American Party. 
At the time of the Republican Party's founding in 1854, all of Massachusetts's congressional representatives but Sumner were members of the nativist Know-Nothing Party. However, Banks's role as chairman of the 1856 Republican National Convention, his active support for the Republican presidential nominee John C. Frémont in 1856 and his focus on anti-slavery legislation as Speaker put him at odds with his party. Following the Democratic victory in the 1856 elections and the Dred Scott case in 1857, the national American Party organization collapsed, and most Northern members joined the nascent Republicans. In 1857, Banks ran as a Republican against incumbent Know-Nothing Governor Henry J. Gardner and won a decisive victory.
Republican Party (United States)
The party's founding members chose the name Republican Party in the mid-1850s as homage to the values of republicanism promoted by Thomas Jefferson's Republican Party. The idea for the name came from an editorial by the party's leading publicist, Horace Greeley, who called for "some simple name like 'Republican' [that] would more fitly designate those who had united to restore the Union to its true mission of champion and promulgator of Liberty rather than propagandist of slavery". The name reflects the 1776 republican values of civic virtue and opposition to aristocracy and corruption. It is important to note that "republican" has a variety of meanings around the world and the Republican Party has evolved such that the meanings no longer always align.