I figured out a solution to my problem. You can use the 'Parse Path' tool under the 'Insert'/'Model Only Tools' menu in Model Builder to extract the base name of the input feature class and store it as a variable. Then when using 'Calculate Field' on a joined table, you can refer to the base name of the input field with the stored inline variable. Below is an example. In this example Im joining a user specified "Subbasins" feature class with a "hydrostrms" feature class, and then calculating the "CumDrnArMi" in "Subbasins" field based on an existing field in "hydrostrms". Since the "Subbasins" is a user specified, the actual name of the feature class may vary.
The Model Builder image shows the 'Parse Path' tool used to extract base name of parameter input for "Subbasin" and store it as "nmSubbasin". The field calculator image shows how field name of the joined table is specified with in-line variable substitution using %nmSubbasin%.
[ATTACH=CONFIG]29155[/ATTACH]
[ATTACH=CONFIG]29157[/ATTACH]