The image of the American Indian used by European societies is a complicated question, and I'm not the best to answer it, but I can speak to the ship naming question at the very least.

So something to keep in mind is that the Cherokee were allies of the British in various colonial wars, including the American war of independence, and had been/were considered one of five "civilized" tribes by early settlers. That designation has to do with the fact that they fairly quickly adopted some European customs, including Christianity, slavery and literacy, and that they intermarried with early settlers. (The idea of the "civilized" tribe is fraught with peril, not least because the division between "civilized" and uncivilized is highly dependent on a particular European worldview, but that's a very brief overview.) The idea that native tribes were "noble savages" who lived in a state of nature took hold in some parts of Europe after the discovery of the new world, but the esteem in which native tribes were held was very situational and waxed and waned depending on the goals and conflicts of the people involved, both native and European.

Something that also could be considered here is that it was fairly common for early settlers, and even people in the present day, to adopt iconography from native tribes -- consider the Boston Tea Party participants dressing up as Mohawks, to identify with what they saw as a "noble" American tribe, or even the current persistence of native American mascots for sports teams. So naming a ship after a tribe isn't that surprising.

Separately, I would urge caution in describing ships built during the Napoleonic period as belonging to a "class." A common design theme might have been approved by the Admiralty, but the ship construction practices of the time were such that it was unlikely for any two ships of a "class" to be identical, though they would be broadly similar. Much of that has to do with the fact that an individual shipwright would use written plans or sketches very much as a set of suggestions, not as a rigid document to be adhered to. And ships were often modified throughout their service life, with the Beagle itself having a third mast stepped to make it into a ship-rigged sloop, not a brig-rigged sloop.

jumping off question:

ww1 onward american military focus on native symbols and names for weapons seems focused on plains indians and the mythic idea of the warrior brave from groups like the souix or apache compounded by the fact that indians (really plains indians i would argue) were percieved as naturally great athletes (like some people view black athletes today).

so was this sort of conception around in the early 19th century as well for british and us military? If it was it would address op's last sentence considering "noble savages" aren't bad military symbols.