What is the name of the thick, rich pork bone broth ramen style?

The thick, rich pork bone broth ramen style is tonkotsu ramen.

Tonkotsu means “pork bones” in Japanese, referring to the broth's defining ingredient. The bones are boiled vigorously for many hours—sometimes up to 18—so fat, collagen, and marrow emulsify into a cloudy, creamy-looking soup. Aromatics such as garlic, ginger, onion, and green onion may be added, along with pork back fat or pig's trotters.

The style originated in Kurume, in Fukuoka Prefecture on Japan's Kyushu island. Food vendor Tokio Miyamoto is credited with inventing it in 1937, while the milky appearance was later associated with broth that had been accidentally overcooked. In Fukuoka, a closely related regional name is Hakata ramen.

Tonkotsu is often served with thin noodles and chashu pork. Many shops let diners choose noodle firmness, from regular futsu to very firm barikata or harigane. A frequent mistake is confusing tonkotsu with tonkatsu: tonkatsu is breaded fried pork, not ramen broth.