Captain April's Enterprise
For more on the subject, see Indian Nicknames for Military Craft.
Also note the egregious Eurocentrism of this class name. The Federation is supposedly an interstellar alliance of dozens of alien races. Can you imagine the justification used to select the name "Cherokee"?
What did they do? No, they didn't found a vast empire or make startling scientific discoveries. In fact, only about 5% of the Earth's population has ever heard of them. Most people couldn't tell a Cherokee from a cherub or a cheroot.
Cherokees are important because the white-skinned humans who dominate the Federation almost exterminated them once. No, wait, this will make sense once I'm done. The Cherokees were proud warriors, and by almost exterminating them, we proved the white-skins are proud warriors. By extension, everyone on Earth and throughout the Federation is a proud warrior also.
Because we "honor" the Cherokees, we don't have to think about how we almost exterminated them. Similarly, when we offer assistance and technology to primitive worlds in exchange for their resources, we don't have to feel bad about corrupting their indigenous cultures. Once they join the Federation, they'll become honorary Cherokees too.
Now do you understand why we're naming the starship class after the Cherokees rather than one of the thousands of warrior cultures on your planets?