When my wife receives a text it also registers on the mac how do we stop it?

I have an iPhone 11, an iMac and my wife has an iPhone SE. When some one sends her a text it also appears on the iMac. I tried going into messages/ preferences/accounts and un ticking her mobile number and that does not work but if you click the box sign out then no messaging works on the iMac?

As per previous reply if I change her iCloud account then will that stop her receiving calendar and contacts updates and stop her downloading photos to the iMac?