The obvious answer is Azeroth is not Earth. But CM Drysc went into a bit more detail, giving some insight into world creation along the way:
There are many names in World of Warcraft that are derived from something they're intended to resemble, either literally or satirically. You could argue that it helps with recognition of what it's intended to represent, especially in literary fantasy. While Azeroth isn't Earth, it's obviously a fantasy based on Earth, humanity, struggles within societies, etc. and in some cases familiar animals may be adapted to the world... of Warcraft. There's something to be said about influence of our world on our attempts to create fantasy or that which we haven't seen, but that's really another discussion entirely.
They could have been called Stripes, or Chazzwuzzers, but would that change what they're intended to represent? There's definitely a need to ground players in a world with things they can relate to, particularly in games that are intended to represent a living world. Many games use a human or at least bipedal protagonist that you control, and that's by no accident. It becomes easier and easier to be drawn into a world, to experience and enjoy something when you aren't constantly working to justify what you're seeing.
I, for one, like the Africa but not Africa feel of The Barrens. Incorporating familar images into my fantasy gaming experience does make it easier for me to immerse myself into the world. And there are plenty of dragons and dinosaurs around to keep the world fantasy enough for me. But, for some, it seems that the similarities are pulling them too much out of their fantasy realm and into our own.
Do the similar creatures but different names help or hinder your immersion into Azeroth? Do Zhevras/Zebras look better with or without horns? Who would trademark an animal name, anyway?