Suppose you have a department table with DepartmentID as primary key, and an employee table with DepartmentID as a foreign key. You can then use the fact that these columns have the same name, to perform a natural join that allows you to omit the column name from the query. (I'm not commenting on whether you should or not - that's a matter of opinion - just noting the fact that this shorthand is part of SQL syntax.)
There are various other cases in SQL syntax where you might refer to the column names with expressions like employee.DepartmentID = department.DepartmentID. Are there any other cases where some kind of shorthand allows you to use the fact that the columns have the same name, to omit the column name?