The easiest way to get it in a design table is to create two configurations with different values and then create the design table and let it auto generate the columns. Once you have done that you can open up the design table and find the column name.
One way to find out how to do it with the API is to manually do it while recording a macro and look at the code that is generated. Basically two things need to be done to the configuration: the part number source needs to be set to the alternative name, and the alternative name needs to be set. The following subroutines do this for the current configuration.
Code:
Sub setBoMPartNumberSource(document As SldWorks.ModelDoc2)
Dim cfg As SldWorks.Configuration
Set cfg = document.ConfigurationManager.ActiveConfiguration
cfg.BOMPartNoSource = swBOMPartNumber_UserSpecified
End Sub
Code:
Sub setAlternativeName(document As SldWorks.ModelDoc2, alternativeName As String)
Dim cfg As SldWorks.Configuration
Set cfg = document.ConfigurationManager.ActiveConfiguration
cfg.AlternateName = alternativeName
End Sub
I have had some problems with the part number source not always taking, but have not bothered to track it down. This should get you started though.