The title comes from the last line of the novel, when an old Native American says to a gathered crowd: "I have lived to see the last warrior of the wise race of the Mohicans." We guess Cooper thought The Last Warrior of the Wise Race of the Mohicans was a little wordy.
This seer guy laments that he remembers the Mohicans from back when they were a super-populous tribe, but that the encroaching white presence on Native American land (you know, the entirety of the American continents) has destroyed a once-proud people. And he didn't even know about white settlers giving Native Americans smallpox-infected blankets.
Although The Last of the Mohicans refers to an actual person named Chingachgook, it would make no sense to have titled the novel Chingachgook, because a) how do you pronounce that? and b) the text is about the demise of an entire system of life, best symbolized by the idea that Chingachgook is the last of his line, "the last of the Mohicans."
Yep: this book is all about how much white settlement of the Americas sucked. Leave your happy-go-lucky first Thanksgiving fantasies of Native American/European unity at the door, folks.