Shouldn't your method names usually be verbs to start with? Like your example, you could just use the verb
Pay instead of
As for how you might use any of the verbs you list (Execute, Do, Run, Perform), I don't think they are necessary at all. They do not convey any additional information. The fact that you are calling (or executing or doing or running or performing) a method is implied by your syntax.
If you'd like to indicate to the caller that your method may return before the action has completed, there is a convention for that in .NET: Begin* and End*.
The only exception I can think of is if you have an abstraction for any general process. In that case, you'll be forced to use a verb such as Execute or Run, since what you're actually doing isn't yet defined.