They don't call themselves the New Avengers. I don't think they even call themselves the Illuminati, that's a Stark thing, IIRC. The New Avengers was on their mini-series title, perhaps because that is where they first appeared, New Avengers #7, but more likely as branding to sell more books, as you said. I look at this in the same way. For whatever reasons, Store owners and fans are going to pick up a New Avengers book, more than they will an Illuminati.
Yeah, I'm hoping Hickman give Strange and Namor stories of their own in New Avengers, and they'll have more of a chance to shine. Ditto on Black Bolt, but I know he's got a story playing out. Buying and keeping my fingers crossed!