How can my wife and I share the same iCloud but have separate iPhones with unique identities?

My wife and I share the same iCloud. When my wife changed her iPhone my daughter did it and paired my phone to her new one. Since then my details within our iCloud didn’t exist. It was just my wife even though I had full working use of my phone , with the exception of caller and message id, we were deeemed to be the same .

find iPhone didn’t work , we couldn’t use the same apps at the same time , it goes on

i have now changed my phone . I backed it up on our iCloud using my laptop , and when I set up and paired with my phone I was even able to change my name back. Hurrah.

however, it immediately changed my wife over as well to be me and now i even get a text from her that comes through as me. So we are even worse off than we were before.

is there a technical way we can keep the same iCloud (changing over would be a nightmare for one of us) but have individual phones for each of us ?

Please Help!!

[Re-Titled by Moderator]