I am trying to bulk load a collection of shapefiles into empty feature classes in ArcMap 10.2. The issue here is that the names of the shapefiles and the feature classes need to match up. Is there any way to make this happen in Model Builder or arcpy?
Take a look at this tool Feature Class To Feature Class (Conversion), the help section contains sample scripts if you want to go the arcpy path.
Right clicking on the tool reveals a "batch" option, you can set the names how you want.