Thanks for the reply Rick.  I'm using the defined names to provide
scrolling chart functionality.  My names and ranges are a bit more
complex than simple cell ranges and look like the following:

SPARE2_RWCFR_ScrollVal   ScrollVal!$C$26

SPARE2_RWCFR_ZoomVal   ScrollVal!$D$26

SPARE2_RWCFR_ChartX   OFFSET('Data Input'!$C
$298,0,SPARE2_RWCFR_ScrollVal-1,1,SPARE2_RWCFR_ZoomVal)

SPARE2_RWCFR_12MA   OFFSET(SPARE2_RWCFR_ChartX,33,0,,)

etc

I'm assuming that the code you have posted should still work despite
this.  I've changed the code to:

Sub AssignNames()
 Dim X As Long
 Const StartRowForTable As Long = 1
 Const EndRowForTable As Long = 3
 Const ColumnForNames As Long = 1
 Const ColumnForRanges As Long = 2
 With ThisWorkbook.Worksheets("Sheet3")
   For X = StartRowForTable To EndRowForTable
     ThisWorkbook.Names.Add .Cells(A,
ColumnForNames).Value, .Range(.Cells(B, ColumnForRanges).Value)
   Next
 End With
End Sub

inserting my Worksheet name and "A" and "B" to define the columns on
the sheet that contain the names and references.  The code is failing
with a runtime error 1004 on the last line.  Have I done the right
thing by placing the names of the column headers (A and B) in the
places where you had the X or should I be doing something different?

Thanks Rick.