When you were able to type in Wilson, you were naming the household. It wasn't naming the Sims themselves. The family surname is Diaz because that's the one who proposed. If Wilson had proposed, it would be Wilson. At the time of marriage, you got a screen letting you choose which house they would live in and who would live there. This is where you typed in Wilson. In the game the name of the household can be the family name or something else, for example "Single Moms." Next, there's the file name, which is what you changed when you did Save As. That's just the name you give the game file so you'll know what it is.
Here's how to change things:
To change the family surname, go to City Hall during normal business house and change your Sims' names.
To change the name of the household, go to Edit Town from the ... menu button in the lower left corner, select your house, then change the name.