How do I change letters of a word or name on click?

The simplest way to do this would be to convert the string to a character array, "mutate" the array, and change it back.
That's pretty simple:

string output = new string(Mutate(input.ToCharArray()));
...
private char[] Mutate(char[] data)
   {
   ...
   }

The Mutate method isn't difficult either: use the Random class to generate a value between 0 and 25, and use that as an index into an array of letters:

private string letters = "abcdefghijklmnopqrstuvwxyz";

(Because a string is a collection, you can use an index on it to retrieve an individual character)
Decide which letters to change, and do it!