The states which are in the Northeast region of the United States are:
New York
Maine
Vermont
New Hampshire
Massachusetts
Connecticut
Rhode Island
Here are their capitals and the meaning behind their names:

New York’s capital is Albany.
New York was named by the British to honor the Duke of York and Albany, the brother of England’s King Charles II, when New Amsterdam was taken from the Dutch in 1664. New York became the name of the state and the city.
Maine’s is Augusta
Maine is really not known how the name for this state originated. One theory suggests that the state was named by French colonists after the French province of Mayne. Another mentions that “Main” was a common term to describe a mainland.
Vermont’s is Montpelier
Vermont is an English form of the name that French explorer Samuel de Champlain gave to Vermont’s Green Mountains on his 1647 map. He called them “Verd Mont” meaning green mountain.
New Hampshire’s is Concord
Captain John Mason received a grant for land in 1629. He named this land New Hampshire after the English county of Hampshire where he had enjoyed a number of years as a child.
Massachusetts is Boston
This state was named after the Massachusetts Indians that lived in the Massachusetts Bay Region. Massachusetts means “large hill place.”
Connecticut’s is Hartford
Connecticut was an established name early in the 1600’s in particular reference to the Connecticut River. The word itself was translated from the Indian name “Quinnehtukqut” and means “beside the long tidal river.”
Rhode Island’s is Providence
Rhode Island was named by Dutch explorer Adrian Block. He named it “Roodt Eylandt” meaning “red island” in reference to the red clay that lined the shore. The name was later anglicized when the region came under British rule.