Indexes with the same object_id but different names
The Object_ID belongs to the object the index belongs to, such as an indexed view or a table.

When you look at the object_id in the sys.indexes documentation


  object_id  - ID of the object to which this index belongs.


If you want to uniquely identify the index you need the Object_ID + index_id columns or the index_id for a specific object_id.

To verify this, you can add the OBJECT_NAME() function to your query

SELECT
  count(object_id) AS count,
  object_id,
  OBJECT_NAME(object_id),
  min(name) as name1,
  max(name) AS name2
FROM
  sys.indexes
GROUP BY object_id HAVING COUNT(*) &gt; 1 ORDER BY count;