Is there a formal name for an artwork such as this?
If you're referring to the technique, that's Stippling or Pointillism if made in color. Images created in this style are composed of numerous dots that form a picture if viewed from afar.


  Stippling is the creation of a pattern simulating varying degrees of solidity or shading by using small dots


rebusB helpfully pointed out that it seems to be a picture created in Photoshop or similar software. That makes is digital art, no matter what other technique it resembles. The reason is that creating artwork on a computer is fundamentally different from creating the same artwork with paint or pencils.

If you're referring to the content of your image, unfortunately I cannot help you. It might be Expressionism, but I'm not sure it can be categorized clearly as any art form or style because it doesn't have much to categorize. Don't get me wrong, it's not bad or anything, it's just not enough there to call it "realism" or "neo-classicism" or anything like that.