What if you remove the quotes around @sqlquery?

ALTER PROCEDURE [dbo].[usp_Names]

(@ID int)

AS

DECLARE @TaskOutFile VARCHAR(255)

DECLARE @sqlquery VARCHAR(100) = 'select * from dbo.Table where ID=@ID';

SET @sqlquery = REPLACE(@SQLQuery,'@ID',@ID);

Select @TaskOutFile = 'C:\' +@ID+ '.html'

EXEC sp_makewebtask @outputfile =@TaskOutFile , @query = @sqlquery;