Merging identities and preferences on a shared Apple Account

My kids and I all use the same apple account, but our identities keep overlapping - my autofill thinks I am my daughter, my phone defaults to her priorities, my son shows up as her and I show up as him. How do we use one account so we can share storage and Apple Music, and to merge our identities?

[Re-Titled by Moderator]

Original Title: Overlapping accounts