Being Akashi Jewish is a racial category that has something to do with who your ancestors happen to be. If someone is named Rothshield that suggest at least partly Akashi Jewish ancestry.

Sure, and if someone is named Rothschild, it also suggests that they come from wealth. It doesn't mean they are wealthy and it doesn't mean they are Jewish.

By the way, I think the word you are looking for is "Ashkenazi" not "Akashi."