I don't believe that you can add report content to add the name of the zone that a surface belongs to. There is a list of pre-defined summary tables, including the Envelope Summary that you mentioned, as well as custom tables that can contain any output variable or meter. However, there are no output variables for "Parent Zone of Surface" or something similar, as these custom tables are meant to look at dynamic outputs that change each timestep.

You can use an Output:Surfaces:List object that appears to include a "Detailed Surface Data Report" option to add content to the EIO output file about surfaces -- including parent zone names. However, this would be difficult to interpret as the EIO file is text-based.

An alternative would be to provide clear indications to the parent zone name within the name of all surfaces. That way, when you look at the Envelope Summary tables, you know what zone each surface belongs to. DesignBuilder (an interface for EnergyPlus) does a great job of automatically applying such a surface naming scheme. Below is a screenshot example of the Envelope Summary created by a DesignBuilder simulation.