Simple:
DateTime dt = DateTime.ParseExact(evendate, "dd/MM/yyyy", CultureInfo.InvariantCulture)
The "format" you supply to ParseExact or TryParseExact is the format of the input string, not any eventual presentation format you might apply. DateTime values don't have "a format" - they are stored as a number of ticks since a predefined point in time.
To format it for display, you have to convert it to a string. For your required format:
string formatted = dt.ToString("yyyy-MM-dd");
Will do it
[edit]Typo[/edit]