Works now also with patches transformator. If you use patches9602 transformator, you will get this warning:

# Warning: 'patchesJson6902' is deprecated. Please use 'patches' instead. Run 'kustomize edit fix' to update your Kustomization automatically.

kustomization.yaml

patches:
  - target:
      group: kustomize.toolkit.fluxcd.io
      version: v1beta1
      kind: Kustomization
      name: name-i-dont-want
    path: patches/kustomization-managed.yaml

patches/kustomization-managed.yaml

- op: replace
  path: /metadata/name
  value: name-i-like

Thanks to @Mafor for the initial solution! My version is just an update, using kubectl v1.27.0.