Cannot delete created excel table

Highlight all of the cells in the table (and only those cells) then click the Convert to Range button in the Table Tools/Design tab (screenshot below).

Now that this data is no longer grouped as a table, it will appear in the Name Manager as separate columns/rows (depending on how you defined the range) with the delete button no longer greyed out.

As I understand, in Excel 2010 (Windows), you cannot delete a table using the Names Manager. Your only option here is to pick any cell or select the existing table name (eg Table1, Table2, Table3, etc.) and convert the table back to a range. One you have done this, the table will disappear from the names manager. Then you can go ahead and create a new table.