set tb = ActiveDocument.GetSheetObject("TB01")
set tbp = tb.GetProperties
set cols = tbp.Layout.ColLayouts
cols.Item(0).Label.v = "New Name"
This is for a TableBox with ID = TB01. This changes the first label. Modify the number in Item(x) to the column you want to change (it starts with 0). Cols is an array, so you can cycle through the list if you would like. Check the APIGuide for more information.
The macro is a little different when working with a chart. For some reason, on a chart, the Dimension Label Attribute is called Title. Try this:
set chart = ActiveDocument.GetSheetObject("CH01")
set cp = chart.GetProperties
set dims = cp.Dimensions
dims(0).Title.v = "Test"
Similarly to the above, the dimensions are an array, so you will need to choose the right element or you can loop through them.