Q: Two phones, one AppleID, getting each other's calls and texts

We have two phones on one Apple ID. We are receiving each other's texts and phone calls.

Apple Support told me that each phone should have it's own Apple ID. I followed directions provided but ended up with....two phones and one Apple ID. It seems that when I created the second ID, I was really just renaming the first one.

As I dig into this issue, I suspect that I don't actually need two Apple IDs, rather I need to distinct phone names.

Is there an expert out there who can advise me? Obviously our goal is to receive only our own calls and messages.