Turns out I just wasn't sure what I was looking for in the Object Properties. What I wanted was "Style", which shows the name of the object in the model from the Resource Manager. If I select on "Style"'s dropdown, I can select "Edit Style" and then it'll open up some options for me from the object within the Resource Manager. I just didn't know that "Style" = the name of the object within the Resource Manager. Sometimes it all comes down to syntax and I'm still figuring out how Vectorworks names things compared to AutoCAD or Revit. Example, Vectorwork's Object Styles seem to be the same as Components from CAD or Types from Revit.