Still wrong to start the name of a user stored procedure with sp_?
This is fairly easy to test yourself. Let's create two very simple procedures:

CREATE PROCEDURE dbo.sp_mystuff
AS
  SELECT 'x';
GO
CREATE PROCEDURE dbo.mystuff
AS
  SELECT 'x';
GO


Now let's build a wrapper that executes them a number of times, with and without the schema prefix:

CREATE PROCEDURE dbo.wrapper_sp1
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @i INT = 1;
    WHILE @i &lt;= 1000
    BEGIN
      EXEC sp_mystuff;
      SET @i += 1;
    END
END
GO
CREATE PROCEDURE dbo.wrapper_1
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @i INT = 1;
    WHILE @i &lt;= 1000
    BEGIN
      EXEC mystuff;
      SET @i += 1;
    END
END
GO
CREATE PROCEDURE dbo.wrapper_sp2
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @i INT = 1;
    WHILE @i &lt;= 1000
    BEGIN
      EXEC dbo.sp_mystuff;
      SET @i += 1;
    END
END
GO
CREATE PROCEDURE dbo.wrapper_2
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @i INT = 1;
    WHILE @i &lt;= 1000
    BEGIN
      EXEC dbo.mystuff;
      SET @i += 1;
    END
END
GO


Results:



Conclusions:


using sp_ prefix is slower
leaving out schema prefix is slower


The more important question: why would you want to use the sp_ prefix? What do your co-workers expect to gain from doing so? This shouldn't be about you having to prove that this is worse, it should be about them justifying adding the same three-letter prefix to every single stored procedure in the system. I fail to see the benefit.

Also I performed some pretty extensive testing of this pattern in the following blog post:

http://www.sqlperformance.com/2012/10/t-sql-queries/sp_prefix