Legal Question in Appeals and Writs in California

Dismissing the appeal long before it's argued might work, assuming that you're the appellant and that no one else is asking for relief in the same appeal. Otherwise, unless you're a minor, you probably can't keep the decision and your name out of search results.

Court decisions are public records, and California's appellate courts make all of their decisions available online. Some get distributed more widely than others. That's especially true of the modest fraction of cases the courts make citable; those cases will be officially published. Some non-citable cases also attract a lot of attention, though most don't. But even if the decision in your case ends up being obscure there will be no way to keep it completely out of the public eye or to prevent Google, et al., from processing it.

Good luck.