How do I change the Apple ID associated with an iphone?

So, I have an apple id, and until now my wife and I have shared it. So both my iphone and hers use the same apple id. This seems to be a mistake, in that now I see her photos, texts and recent calls on my phone, and vice versa.

I am new to the apple world so, when I had my android device, and she had her iphone all was well. I may end up going back to that scenerio, but would like to try and solve this.

Anyways, the solution seemed simple to me, just create a new apple id for her and associate her phone with that id, while I retained mine.

The problem is that I don't seem able to change the apple id associated with her phone to the new apple id we created for her. It seems this should be doable from the 'AppleID, iCloud, Media & Purchases setting, but it's not so straightforward. One cannot simply click on the Apple ID at the top and change it. Also, if I try to change the email associated with the phone, to the new one I just created, it indicates an error telling me it's already in use.

Somewhere, somehow, this must be easy. Do I have to reset the phone ? That seems extreme.

Help.