There's various trendy names and variations of that type of diet. But it's a really simple way to eat. I am not completely strict on any diet at the moment, but I generally go no sugar and no dairy, avoid most packaged foods, and the difference I feel is amazing. I don't completely eliminate gluten, I just make sure I only eat good sources of it. And I actually am allergic to wheat, it's not a trendy thing for me. I always figured it was more the horrid bleached white flours used in most of our foods though, and when I stuck to only occasionally eating good sourced products, I had no issues.
The diet is not restrictive though. I know people find cutting dairy out hard, but once you do it it's really easy. And I am someone who likes it. As for sugar, the results you see when you cut it out make that easy too. But you can eat some fruit, all the veg you want, and good meats. And as you mentioned, you need to make sure you are getting healthy fats, which is a key. That's not really a tough diet.
My policy is that if I go out for a night with friends, I just do what I want diet wise. At home, I just stick to basics.