"Wagyu Beef" is how reputable meat-sellers describe Kobe-style beef.
Here's an ad from Allen Brothers:
"Just as Champagne can only be used when describing sparkling wine from the Champagne region of France, the name Kobe is reserved exclusively to describe Wagyu cattle raised in the Kobe region of Japan for more than 1800 years. Hence, any Wagyu cattle raised outside of Kobe must go by the names Wagyu or Kobe-style."
The guy who wrote that article doesn't think much of "Wagyu" either.