Q. Are reverse italics [i.e., roman text in an otherwise italic context] used when a legal case includes names of newspapers that would normally be italicized on their own? Thank you!
A. The name of a newspaper or other periodical would be italicized in the name of a court case—just like the name of any other entity. The Bluebook, a widely used citation guide that we recommend for citing court cases and the like (see CMOS 14.269), includes a relevant example: Seattle Times v. Univ. of Wash. (see section B10.1.1 in the 21st ed. of The Bluebook [2020]).
That Bluebook example is intended to illustrate two principles: (1) an initial The in the name of a party to a cited case can be omitted (a rule that applies to both names in the Seattle Times case), and (2) abbreviations can be used for certain terms, including state names and words like “University.”
And though that example isn’t supposed to show the use of italics for case names (which in Bluebook usage depends on context), it does suggest that a newspaper name within the name of a court case doesn’t merit any special typographic treatment. That’s probably because the name “Seattle Times” is, in this context, that of a publishing company rather than a publication (publications don’t argue cases, but their publishers do).