were they associated with any war?
Yes, the King Philip's War.
Massachusett
The Praying Indians endured attacks by their kinsfolk that supported Metacomet. Just before the winter of 1675, colonial militia rounded up the Praying Indians forcibly interned them on Deer Island in Boston Harbor. Similarly, the Mattakeeset were marched to Clark's Island. With little food and clothing, many of the Indians perished from starvation, exposure and disease. Many of the Praying Indians were recruited to serve as scouts, guides and to fill the ranks of the colonial militia, with a regiment recruited by Daniel Gookin sent to face Metacomet's warriors at Swansea, but it is known that other Massachusett aided the colonial militias in Lancaster, Brookfield and Mount Hope battles of the war. Despite early victories, Metacomet was weakened by lack of resources and the help of the Praying Indians to the English. 
with which colony is the mayflower compact most often identified Plymouth. who named the colony? Captain John Smith. where is it located? Southeast Massachusetts. how did the aforesaid state get its name? From the indigenous population, the Massachusett.
wiki:12189635
Massachusett [SEP] King Philip's War (1675–1676)
The truce that had existed between the English settlers of the Massachusetts Bay and Plymouth colonies and the local Native peoples was tested. The submission of the local chiefs to the respective colonial governments and adoption of Christianity allowed the Indians to seek redress in the English court system and removed one of the prejudices against them. The Praying Indians of Natick were brought to court several times by the English settlers of Dedham that claimed some of the land, but with Eliot's assistance, most of these attempts failed. Most of the time, however, the Indians failed, as some of the Indian interpreters and chiefs ceded lands to curry favor from the English to maintain special privileges, such as the Nipmuc John Wampas, who betrayed the Nipmuc and Massachusett people by selling land to the settlers to which he had no claim, but these sales were upheld in later court challenges.