When we speak of "the name of the game," we are referring to the essential factor or core principle of a situation or activity. Synonyms for this expression could include "the crux of the matter," "the heart of the issue," "the essence," "the key element," "the central focus," or "the defining factor." This commonly used expression basically highlights the most important aspect or feature of a particular situation or activity. So, whether you are discussing business, sports, or everyday life, you can use these synonyms to describe the most crucial element of what's happening or what you're talking about.