TLDR:
Unless we are talking about TryParse, methods should not start with Try.
A method returning null should follow the 'OrDefault' pattern.
There is currently no evidence/guidance that the TryParse pattern (which IS documented) was intended to become TryX.
TryParse makes sense because there really is only one reason for failure (a bad input string) TrySomething does not make sense if there are multiple reasons for failure and doing so encourages bad error handling.
Explanation
There's an interesting slant to this that I think we have to consider and I think it's a stretch to assume the TryParse pattern can be generaized to TryX. The TryParse pattern as it is named by Microsoft is named specifically with 'Parse' for a reason - using 'TryX' might be considered an anti-pattern and they are trying to avoid expansion of it's use.
If the Tester-Doer pattern tests and then executes, then an execute and then test pattern might be called Doer-Tester. However, there is a fundamental difference. In a Tester-Doer the doer still throws an exception on failure. This is not the case in this TryX Doer-Tester.
This presents a pit-of-success problem. You now have code that might do absolutely nothing. At best you don't know why it failed. In the case of a forgotten if/test, it creates odd, red-herring bugs farther into the code.
I'm not afraid to admit that this is conjecture. But when I first saw "TryParse" as a pattern name, I thought how could they be so lazy and be so specific...and then I thought maybe they weren't.
With parse, there is really a single reason that an exception can be thrown - that the input string was not in the correct format. And so it is understood what a return value of false means.
But in a generic case, that can't be said - there may be multiple failure reasons. You are very quickly getting into other best practice considerations and debates like the case for throwing exceptions and minimizing try/catch blocks and the associated logging.
I'm not saying that there's isn't the occasional application of this 'pattern'. I suppose there are places in background threads and during shutdown or logging attempts where if it goes bad there, your options for recovery grow slim. But these scenarios are pretty rare. And is there really nothing you can do? Are you sure the try/catch shouldn't be higher up? I think those are the questions we're meant to ask before we rely on a pattern that lets us write methods that may or may not do what they are supposed to do.