In character, the names of canon species remain the same, this is a Star Trek universe, even if it is an alternate furry one. My biggest concern when it comes to legality is copyright infringment, and while complicated it matters how much we borrow and how much we transform what we borrow into a new form. Borrowing the names and general feel of the aliens is considered more perhipheral, while canon characters and stories are closer to the "heart" of the original work. So we tend to avoid talking about canon characters and stories more than tangential references. For instance, we'll never run into Kirk or Picard or any Enterprise. Deep Space 9 is harder to avoid as it was pivotal in the Dominion War and still gards the wormhole, but otherwise, if it's on the screen for most of the episode, we avoid it. The universe is more than big enough that we don't need to interact with canon characters or follow in their pawsteps.
There is nothing wrong with Earth or any derivative. Just there are no Humans. The closest word is "humane", which is the root word of "humanitarian", so that word is alright, other than that it should be easy enough to avoid the word human. "Humanoid" would formally be "Anthroid", more casually "Anthro", or perhaps a more specific term such as "biped" (excludes 'taurs and tripeds like the Edosians), "intelligent beings" or "civilized beings".
If your character is a Terran, they will probably use their common local name of their homeworld, "Earth" even though the more intergalactically recognised version is Terra, and most aliens are familiar with both names (or it gets translated by the Universal Translator. Whether you call yourselves Terrans or Earthers doesn't matter to aliens (though the later tends to be used more derogatorily) you will probably refer to the Vulcan offshoot as Romulans. This is understood by everyone familiar with both the Federation and the Romulans. While the Romulans refer to themselves as the Rihannsu. So yes, most in the Federation would still call it the Romulan-Earth war. Though the Rihannsu call it something different.
EDIT:
Some monospecies factions in Canon are represented by multiple species in our universe. For example the Klingon Empire now consists of Targs, mIloD (Saber bears), Sargh Equines, Whitefang wolves and at least four other species. See
Species suggestion list for specifics. And feel free to suggest other species for canon factions.
