Apparently it's garlic added to it. That's not special, everybody adds garlic to everything. We added that shit to butter, it changed seafood dinners forever and you don't see it getting a fancy name.
Lol. It's supposed to be shit other than garlic, like "black pepper aioli" or "madras curry aioli" or "champagne vinaigrette aioli." But yeah, I guess if you want pretense points for "garlic and mayonnaise" just calling it straight aioli fits the bill...
Wikipedia dishing out the truth: Aioli here is basically garlic sauce. Not just 'oh, there is a hint of garlic in there', no, there should be 'my bad breath can kill a nation' amounts of garlic. I love it. But I also combine it with Doritos, so maybe my culinary authority isn't worth much.Since the late 1980s, it has become fashionable to call all flavored mayonnaises "aioli", with flavorings such as saffron or chili.[7] However, purists insist that "flavored mayonnaise can contain garlic, but true aioli contains no seasoning but garlic".[8]