get all characters to right of last dash

You can get the position of the last - with str.LastIndexOf('-'). So the next step is obvious:

var result = str.Substring(str.LastIndexOf('-') + 1);

Correction:

As Brian states below, using this on a string with no dashes will result in the original string being returned.

You could use LINQ, and save yourself the explicit parsing:

string test = "9586-202-10072";
string lastFragment = test.Split('-').Last();

Console.WriteLine(lastFragment);

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