This Singleton Pattern has the advantage to be easy to memorize.
The only really interesting aspect of it is the issue of initialization („lazy or „eager“) and maybe the dependencies between multiple singletons.
But I would like to mention two generalizations.
A Singleton exists once in the whole program. Generalizations can address the uniqueness in two ways. Either the number of instances can be increased from one to a small number or the universe („whole program“) can be changed. What is the universe in a big software system that is running on multiple servers with many processes and components?
Changing from one to a small fixed finite number is quite a routine thing. Java developers are calling this enum, but other programming language often have similar structures or at least allow to build them easily by restricting the generation of objects and creating the whole set of instances statically and making them accessible. I am not talking about the enum of C, C++ and C#.
The other, slightly more complex generalization looks at the „universe“. An application can be distributed and have several parallel processes, not only threads. This would mean dealing with a larger universe, which can become slightly tricky, but some examples of that are actually routine. Think of a database that exists once in the application to allow operating on the same data and keeping them consistent. Frameworks sometimes allow for an application server wide more or less classical singleton that exists once in the whole server landscape but can be accessed more or less transparently. An interesting case that is needed quite often is a global counter. It can be done using a DB-sequence. Or giving disjoint subsets of the numbers that could be generated to different processes and server. Or by using something like a UUID and praying that no collisions will occur. But an application wide singleton might be useful in some cases. Some frameworks are talking about a „bean“ with „application scope“. On the other hand smaller universes are even more useful. A typical example is the „session scope“.
Maybe just understanding these as a proper generalization of the singleton pattern will help in making these frameworks more understandable and more useful. The investment of having started with the most simple design pattern might actually pay off. Looking into some of the other patterns could be a worth while task for the future… 😉