Why clustered index scan?
This table is very small!

It has 20 rows of which 2 match the search condition. The table definition contains three columns and two indexes (which both support uniqueness constraints).

CREATE TABLE Person.ContactType(
    ContactTypeID int IDENTITY(1,1) NOT NULL,
    Name dbo.Name NOT NULL,
    ModifiedDate datetime NOT NULL,
    CONSTRAINT PK_ContactType_ContactTypeID PRIMARY KEY CLUSTERED(ContactTypeID),
    CONSTRAINT AK_ContactType_Name UNIQUE NONCLUSTERED(Name)
) 


Running

SELECT index_type_desc,
       index_depth,
       page_count,
       avg_page_space_used_in_percent,
       avg_record_size_in_bytes
FROM   sys.dm_db_index_physical_stats(db_id(), 
                                      object_id('Person.ContactType'), 
                                      NULL, 
                                      NULL, 
                                      'DETAILED') 


Shows both indexes only consist of a single leaf page with no upper level pages.

+--------------------+-------------+------------+--------------------------------+--------------------------+
|  index_type_desc   | index_depth | page_count | avg_page_space_used_in_percent | avg_record_size_in_bytes |
+--------------------+-------------+------------+--------------------------------+--------------------------+
| CLUSTERED INDEX    |           1 |          1 | 15.9130219915987               | 62.5                     |
| NONCLUSTERED INDEX |           1 |          1 | 13.1949592290586               | 51.5                     |
+--------------------+-------------+------------+--------------------------------+--------------------------+


Rows on each index page aren't necessarily in index key order but each page has a slot array with the offset of each row on the page. This is maintained in index order.

The nonclustered index covers two out of the three columns (Name as a key column and ContactTypeID as a row locator back to the base table) but is missing ModifiedDate.

You can use index hints to force the NCI seek as below

SELECT ct.*
FROM   Person.ContactType AS ct WITH (INDEX = AK_ContactType_Name)
WHERE  ct.Name LIKE 'Own%'; 


But you can see that under SQL Server's cost model this plan is given a higher estimated cost than the competing CI scan (roughly double).



The single page clustered index scan would just need to read all the 20 rows on the page, evaluate the predicate against them and return them.

The single page nonclustered index range seek might potentially be able to perform a binary search on the slot array to reduce the number of rows evaluated however the index does not cover the query so it would also need a potential IO to retrieve the CI page and then it would still need to locate the row with the missing column values on there (for each row returned by the NCI seek).

On my machine running 1 million iterations of the non clustered index plan took 15.245 seconds compared to 11.113 seconds for the clustered index plan. Whilst this is far from double the plan without the hint was measurably faster.

Even if the table was orders of magnitude larger however you may well still not get your expected plan with lookups.

SQL Server's costing model prefers sequential scans to random IO lookups and the "tipping point" between it choosing a scan of a covering index or a seek and lookups of a non covering one is often surprisingly low as discussed in Kimberley Tripp's blog post here.

It is certainly not out of the question that it would choose such a plan for a 10% selective predicate but the clustered index would likely need to be quite a lot wider than the NCI for it to do so.