Here I am studying nonclustered indexes on SQL Server Management Studio.

I've created a table with more than 1 million records. This table has a primary key.

SELECT CustomerName FROM Customers

Which leads the execution plan to show me:

I/O cost = 3.45646
Operator cost = 4.57715

For the first attempt to improve performance, I've created a nonclustered index for this table:

CREATE NONCLUSTERED INDEX [IX_CustomerID_CustomerName] ON [dbo].[Customers] 
(
    [CustomerId] ASC,
    [CustomerName] ASC
)WITH (PAD_INDEX  = OFF, STATISTICS_NORECOMPUTE  = OFF, SORT_IN_TEMPDB = OFF,
IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS  = ON,
ALLOW_PAGE_LOCKS  = ON) ON [PRIMARY]
GO

With this first try, I've executed the select statement and the execution plan shows me:

I/O cost = 2.79942
Operator cost = 3.92001

Now the second try, I've deleted this nonclustered index in order to create a new one.

CREATE NONCLUSTERED INDEX [IX_CategoryName] ON [dbo].[Categories] 
(
    [CategoryId] ASC
)
INCLUDE ( [CategoryName]) WITH (PAD_INDEX  = OFF, STATISTICS_NORECOMPUTE  = OFF,  
SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF,   
ALLOW_ROW_LOCKS  = ON, ALLOW_PAGE_LOCKS  = ON) ON [PRIMARY]
GO

With this second try, I've executed the select statement and the execution plan shows me the same result:

I/O cost = 2.79942
Operator cost = 3.92001

Am I doing something wrong or this is expected? Shall I use the first nonclustered index with two fields, or the second nonclustered with one field (CategoryID) including the second field (CategoryName)?