To change the name of a table:
Select the table in Manage | database | Tables
Type in a new table name for the selected table. The greyed button will now change. Click change and you have changed the name of your table. However, each time you create a new table, FileMaker automatically creates a matching Layout and Table Occurrence of the same name. Changing the name of the table does not change the name of the layout nor does it change the name of the table occurrence. (A table occurrence is the "box" found in Manage | database | layouts.)
Delete layout works just fine in Manage | Layouts, but there's one restriction: There must always be at least one layout in your database at all time. If there is only one layout in your file, you will not be able to delete that last layout until you first create a new layout. You can also rename a layout with the edit button and you can also use this option to link a layout to a different table occurrence.
To learn more about table occurrences and how they control the function of a FileMaker database, see this thread: Tutorial: What are Table Occurrences?