CREATE TYPE dbo.DeptList
AS TABLE
(
  ID INT
);
GO
CREATE PROCEDURE dbo.RetrieveDepartments
  @dept_list AS dbo.DeptList READONLY
AS
BEGIN
  SET NOCOUNT ON;
  SELECT Name FROM dbo.table1 WHERE ID IN (SELECT ID FROM @dept)
  UNION ALL 
  SELECT Name FROM dbo.table2 WHERE ID IN (SELECT ID FROM @dept)
  -- ...
END
GO
Now in your C# code, create a DataTable, fill it in with the IDs, and pass it in to the stored procedure. Assuming you already have a list called tempList and the IDs are stored in id:
DataTable tvp = new DataTable();
tvp.Columns.Add(new DataColumn("ID"));
foreach(var item in tempList)
{ 
    tvp.Rows.Add(item.id); 
}
using (connObject)
{
    SqlCommand cmd = new SqlCommand("StoredProcedure", connObject);
    cmd.CommandType = CommandType.StoredProcedure;
    SqlParameter tvparam = cmd.Parameters.AddWithValue("@dept_list", tvp);
    tvparam.SqlDbType = SqlDbType.Structured;
    ...
}
You can also use a split function. Many exist, this is the one I like if you can guarantee that the input is safe (no <, >, & etc.):
CREATE FUNCTION dbo.SplitInts_XML
(
   @List       VARCHAR(MAX),
   @Delimiter  CHAR(1)
)
RETURNS TABLE
AS
   RETURN 
   (  
      SELECT Item = y.i.value('(./text())[1]', 'int')
      FROM 
      ( 
        SELECT x = CONVERT(XML, '<i>' 
        + REPLACE(@List, @Delimiter, '</i><i>') + '</i>').query('.')
      ) AS a 
      CROSS APPLY x.nodes('i') AS y(i)
   );
GO
Now your procedure can be:
CREATE PROCEDURE dbo.RetrieveDepartments
  @dept_list VARCHAR(MAX)
AS
BEGIN
  SET NOCOUNT ON;
  ;WITH d AS (SELECT ID = Item FROM dbo.SplitInts(@dept_list, ','))
  SELECT Name FROM dbo.table1 WHERE ID IN (SELECT ID FROM d)
  UNION ALL
  SELECT Name FROM dbo.table2 WHERE ID IN (SELECT ID FROM d)
  -- ...
END
GO