I don't think that there is anything wrong with mixing martial arts. I myself studied a mixed art that included Aikido, sort of. (we also practiced in a YMCA) My instructor was very talented and his art was very effective. But as Chris Li pointed out, there are a lot of under qualified people who create their own arts, mis-use names and generally make everyone else look bad. I would advise that you be prepared to meet suspicion/skepticism when discussing your chosen art.
I will have to agree that your instructor's choice in names seems a bit odd. Although I could be mistaken seeing as my knowledge of Japanese is limited to a few trivial words and phrases.
That said, as long as you are satisfied with what you are being taught don't worry too much about the name. If you begin to doubt your instructor's credibility, then maybe you should check it out.