I agree that "name" and "reputation" are essentially the same ideas. But to move from "soul" to "identity" and then arrive at "name" looks like equivocation by way of confusion of catorgories. I also agree "soul" is referring to the whole of a person's self. But while identity in the above quote appears a nice transitional form to one's reputation, 1 Peter 3:20 just says that eight souls were saved. I still can't see how soul begets name. Peter is retelling a story about how eight people were saved from the flood. Those people had names and reputations, but these were a specific consequence of being souls, not synonymous with them.Really? To my mind, a person's "soul" is best understood as a reference to the whole of a person's self or identity (e.g., 1 Peter 3:20). This is also the way the concept of one's "name" was generally understood. I don't see any difference between a person's "name" and his "reputation." It seems to me these ideas are essentially interchangeable throughout scripture.
While nephesh and psuche are used throughout the scriptures in a flexible way, I think their usage retains a specificity of pertaining to life. Never do they lose their relationship to either being a living creature or having the capacity to be so. What you're suggesting seems like: if two people walk up to a road and see tread marks left from a car's tires, and one asks the other, "What is that on the road?" Then the other answers, "That is a car." A name or reputation is something a soul may acquire among other souls, and after his death it still be retained by them or others. While moderns may say something like, "she lives on in our memory," or "in our hearts," regarding her reputation and name, I don't recall the scriptures ever using "soul" in this way.
Will you demonstrate where you find such an exchangeability between "soul" and "name/reputation" elsewhere in scripture?
Grace and peace be with you.