Shouldn't your method names usually be verbs to start with? Like your example, you could just use the verb Pay instead of Perform + Payment.

Edit:

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...