What is the process of changing the last name of the children my wife had before our marriage. I am the only father they know. I have been in the twin boys life since before they were 1 years old. The father is no where to be found, and his name is not on birth certificate. We both agree to have their name changed to my last name. Is this procedure under these circumstances simple?

You need to first establish who the father is and then ask their permission. If you can't find the father a attempt must be made and the process drags out much further.
You are required by law to make a good faith attempt.

I would assume there is no court order of custody, no child support order,

But the father has to be established in court, and the father give permission for name change