When Table is applied to a range it is given the equivalent of a Range Name starting with "Table1". That name, however can be changed on the Table tab of the Ribbon.
Since they're treated as Named Ranges the name of Tables appear in the Name Box @ the left end of the Formula Bar.
As for the delete part of your question: It depends on exactly what you want to delete...
If you simply want to remove the Table effects/features use the Convert to Range tool on the Table tab. It also may be necessary to remove the formatting separately.
If you do want to delete the actual data you can do so just as with any other range of cells by selecting the rage & using Edit> Clear> All.