When you talk about a date range, you normally mean "all dates between 2nd Feb 2012 and 14th Jun 2013" or similar - but your code doesn't try to do that, so I'm left a little confused as to what you are trying to achieve, especially when you describe what you want as "if a user selects say 6th may as the from date and 10th may as the to date,All the names within that date range".
The code you have checks for two specific conditions: "the start date is exactly this date", and "the end date is exactly that date". If you do want a range, such as "the start and end dates must be between the start and end dates" then it's pretty simple:
SELECT * FROM MyTable WHERE created_date BETWEEN @DateFrom AND @DateTo AND todate BETWEEN @DateFrom AND @DateTo
If that isn't what you are trying to do, then we need a better description of what you do expect to happen, perhaps with an example or two.