Drop multiple columns at the same time from a SQL Server table
You're currently looking for a column_name that has different values, so you'll never pass the test. You have to search in different rows to make it work.

    IF EXISTS(SELECT 1
              FROM INFORMATION_SCHEMA.COLUMNS
              WHERE TABLE_NAME='my_Table'
              and column_name= 'ID')
AND EXISTS (SELECT 1
              FROM INFORMATION_SCHEMA.COLUMNS
              WHERE TABLE_NAME='my_Table'
              and column_name= 'Relationship')
      BEGIN
        ALTER TABLE my_Table
        DROP COLUMN 
         ID
        ,Name
        ,Relationship
      END