Peter, I'd agree that it is best to go with what you know in terms of names, but what to tell the student who is asking the names without having set foot in the dojo yet? the point I was making was about beginners who focus on 'the RIGHT way' (you know them, they wander from senior to senior holding a book published by someone in a different style, or a magaizne or internet article, demanding to know why we don't use the 'right' name). I worry when folks who haven't even found a dojo yet are wanting to know answers that a dojo should be providing. Those are the types most likely to get frustrated when they find disagreement between what they read or see in videos and see and hear on the mat.
As for testing, Kat, not to sound like a broken record but ask at the dojo you join. Since you seem to have a fair amount of experience in karate, and have had several different sensei and dojos, then you must know that can vary from sensei to sensei. Some test those they want, when they want. Others only if it is requested. Just ask when you join a dojo, nothing that you read here matters, it is what your sensei tells you. You must realize this from all your previous experience.
Good luck on finding a place to train, let us know how you enjoyed your first class.