In Australia, brokers can hold and manage clients' stocks and other financial assets through two different operating models: CHESS-sponsored model and Custodian model.
CHESS-sponsored:
Under the CHESS-sponsored model, investors receive a unique Holder Identification Number (HIN).
In this model, investors' securities are directly registered under their own name and recorded in the CHESS holdings system of ASX Settlement Pty Limited
Custodian:
Under the Custodian model, the ASX securities are held through an omnibus arrangement by moomoo AU's nominated custodian.
Your securities are well protected with moomoo under both models. It is entirely a personal preference.