I'm struggling to explain it, but some examples are (mention does not imply endorsement!):
- Sir Keir Starmer -> Sir Kid Starver (criticism of his stance on child benefits)
- Benedict Cumberbatch -> Butterscotch Candybatch (surreal humour)
- Financial Conduct Authority -> Fundamentally Complicit Authority (critical of regulatory capture)
- Saddam Hussein -> Sadman Insane (general derision)
These are nicknames, i suppose, but they are a specific kind of nickname.