IMHO, childish is a generous interpretation because the purpose of these nicknames is to strategically dehumanize and diminish the target.
H introduced the nickname “Willy” in his book Spare which puzzled his acquaintances who claimed that H called his brother "Wills". The Sussex Squad ecosystem uses other cruel nicknames such as “Egghead” or “Baldy” to target W.
M intentionally revived the “Waitie Katie” nickname in the 2021 Oprah interview to target C. Omid added “Katie Keen” to the Sussex Squad lexicon, a nickname based on a character from US comics books M has said on record were her favorite to read. Since Omid's Endgame allegations, the SS use a racially charged slur based on a US hate group to viciously target C.
Unsurprisingly, Ari Emmanuel from WME which represents H&M, would have been familiar with this dehumanization strategy from his brother, political operative Rahm Emmanel...and anyone who lived through the 2016 US Presidential elections can see the way in which SS strategy models key aspects of hyper-polarization political strategy, of which Trump is a master.
For example, in the 2016 Republican Primary, Trump nicknamed his current Secretary of State “Little Marco” mocking his height. (A photo from a 2015 campaign event showed the then Senator Marco Rubio, Florida wearing platform shoes). Other nicknames Trump deployed included “Lyin’ Ted” (Senator Ted Cruz, Texas) and “Low-energy Jeb” (Jeb Bush, Former Governor of Florida). Later on, in the general election, Trump nicknamed Secretary Clinton as “Crooked Hillary” as part of a strategy to dehumanize and diminish his political opponents.