I'm pretty well sold on the "singletons are evil" line of thought. Nevertheless, there are limited occurrences when you want to limit the creation of an object. Roy Osherove advises,
If you're planning to use a singleton in your design, separate the logic of the singleton class and the logic that makes it a singleton (the part that initializes a static variables, for example) into two separate classes. That way, you can keep the single responsibility principle (SRP) and also have a way to override singleton logic. (The Art of Unit Testing 261-262)
This pattern still perpetuates the global state. However, it does result in a testable design, so it seems to me to be a good pattern for mitigating the damage of a singleton.
However, Osherove does not give a name to this pattern; but naming a pattern, according to the Gang of Four, is important:
Naming a pattern immediately increases our design vocabulary. It lets us design at a higher level of abstraction. (3)
Is there a standard name for this pattern? It seems different enough from a standard singleton to deserve a separate name. Decoupled Singleton, perhaps?