In January 2016, in the Supreme Court, in the case of Regina (on the application of C) -v- Secretary of State for Justice, Lady Hale said: "the names of the people whose cases are being decided, and others involved in the hearing, should be public knowledge." . . although in that case the party remained anonymous.
I think that the system of precedents could work entirely successfully if parties were referred to by say a four character randomly chosen code. The immigration tribunal works perfectly well with a huge number of anonymous cases. They do not quite roll from the tongue, but they work.
Sometimes I see someone going large on social media sites, but reflecting more than anything else, their capacity for self delusion as identified in a judgment. I go out of my way in reporting cases to concentrate on the point of law explained by the judge. It is rare for a summary of ours actually to say anything deleterious to a party, I try particularly to avoid such.