I'm writing a paper for my high school U.S. History class, and I want to refer to certain Supreme Court cases by just one name after my first naming of the case (for example, I want to refer to Rucho v. Common Cause as Rucho or as Common Cause), but I'm not certain about whether the proper name to use is that of the appellant or that of the appellee, or even whether such a standard exists. I've seen it done before in news sources covering Supreme Court cases, so I know it can be done, but I have seen both used at times. I've tried to search for a solution to my problem online, but have found only references on how to cite decisions in full, at the end of a paper. Any help would be appreciated. Thank you.
How to refer to Supreme Court cases by just one name
In general, subsequent references to a decision can be the first name in the caption of that case.
As an example, you will notice that in the decision Rucho v. Common Cause, 139 S.Ct. 2484 (2019) the court makes an initial reference to Gill v. Whitford (at 2492), and thereafter most of the references to that decision are simply Gill (see, for instance, at 2498, 2501, 2507).
Nate Elredge makes a good point in that there are exceptions. Where the general rule may result ambiguous, another main party in the caption would be mentioned. Using Nate's example of United States v. Nixon, the court's subsequent references to that case in Calley v. Callaway, 382 F.Supp. 650 (1974) is Nixon.
There might be other, harder to find, instances where ambiguity persists. For instance, several unrelated decisions issued by the same court might involve the exact same parties. In those scenarios only the suffix (that is, the numbers following the caption) would distinguish among decisions.