Excel Table headers - field names list not showing when typing

So how did you 'rename' the table? you must click on the table and go to the Table Design tab in the menu and then click in the table name there. IF you highlighted the table and change the RANGE name you defined a RANGE that matches the table area but that is not a new TABLE name. You can check by typing Table1[ and see if the columns come up because excel still thinks that table is named Table1

Here is an image of the Table Design menu with the Table Name box on the left.

Alternatively you can also 'rename' the table using the Name Manager (Formulas Tab):

In the above image is the Name Manager where I renamed Table1 to Table1b but myTable is a range not the Table name (notice how it refers to =Table1b(#All) since the Table name is Table1b and was not changed to myTable)

If this is not the issue, please share a sample sheet we can check more into.