When is "Try" supposed to be used in C# method names?

This is known as the TryParse pattern and has been documented by Microsoft. The official Exceptions and Performance MSDN page says:

Consider the TryParse pattern for members that may throw exceptions in common scenarios to avoid performance problems related to exceptions.

Thus if you have code for which a regular use case would mean that it might throw an exception (such as parsing an int), the TryParse pattern makes sense.

(Corrected) There is official guideline, as Erik suggested.

When I see TrySomething method, I assume it

• doesn't throw
• returns bool
• if I expect value, it is returned via 'out' parameter
• there exists Something method, that allows me to handle any exception myself. (edit, suggested by Jesse Webb)

I think you should use try when you want to proceed. It doesn't matter that a method returns some value or not.

Case 1: if it returns fine, you can proceed in some way.

Case 2: if it does not return: it is still fine; you can proceed in some other way.

And if you expect some value as output of that method then use the out parameter.

Example

int value
if (dictionary.TryGetValue("key", out value))
{
    // Proceed in some way
}
else
{
    // Proceed in some other way
}