Why the name change? It is the Yakuza after all.
No official statement ever made, but I believe it's for consistency's sake.
In Japan, the series is known as
Ryū ga Gotoku, which means "Like a Dragon" in english.
Just like when they changed back Dr. Robotnik to his Japanese name again, Dr. Eggman.
For me "Yakuza" still sounds much cooler name than "Like a Dragon" but of course it wouldn't suit for Ishin title since Yakuza wasn't exist at that time.