Colonists who opposed Britain and wanted freedom were patriots. Colonists who were loyal to Britain were loyalists or Tories. Most of the colonists wanted or didn't want freedom, so there really was no need to a name.
Yes, In the New Jersey Colony the colonists use to say, "If you want freedom of religion and freedom to live your own lifestyle then that is what you will get!" They said this because they wanted to form a colony of freedom and peace. In fact, they opposed war and were known as pacifists.