Do I need to define the same name of the well as it had in its historical values?

Normally you will use the same name, and if it has the same name, the connection is created automatically by pForecast. If you do not have the same name, one option is to select the well name in the “Forecast wells” tab to update. 

Another option is to switch to property view and then select a property, and choose “Wellbores”, then you get a list of radio buttons that allow you to connect each well to a wellbore. 

The third alternative is to import these properties using the existing template, just select to download the template and choose to “Pre-fill template” to get all the existing values and then it is rather easy to updated/correct the wellbore names as needed.