Generally, in law school, in a Supreme Court
case, we abbreviate to the appellant/petitioner (in a
Supreme Court case, that means the first party listed),
or if the appellant happens to be non-unique party
(say, a state or the attorney general) the unusual
party. One party will generally be sufficient.
As for NYT vs. Sullivan, I have heard it discussed
as both _NYT_ and as _Sullivan_.
Something like
_ACLU vs. Reno_ is more difficult. I'd be inclined to
accept ACLU, despite its de facto status as a frequent
litigator, since it is probably the most famous case out
there in which the ACLU is the petitioning party.