I'm all in favor of using abbreviations to shield the identity of litigants in appropriate cases. So even in a civil case (as here), if there are allegations of domestic abuse, personal sexual conduct, etc., and there's a minor child involved, it generally makes sense to omit the actual names of the parties.
Yet this is one of those rare cases in which doing so makes little sense.
The nanny is L.G., the (ex-) wife is M.B., and the (ex-) husband is S.B. It's a celebrity couple and their nanny, with Wife saying that Husband had sex with Nanny, got her pregnant, etc. Nanny then sues Wife for defamation and other torts, Wife files but loses an anti-SLAPP motion, and Wife then appeals.
All lurid stuff, with more in the actual opinion, so you can well understand why the Court of Appeal employs initials.
Though it merits mention that this stuff is all over the press anyway. Like, everywhere.
Unless it just so happens that this is merely one of several nanny-threesome-lawsuit-disputes involving people with the initials L.G., M.B., and S.B. that doesn't involve Lorraine Gilles, former Scary Spice Melanie G., and Stephen Belafonte. In which case, yeah, definitely use initials.
P.S. - FYI, "M.G." loses her appeal.