Utilize your financial knowledge, give your answer or opinion to the input question or subject . Answer format is not limited.

Deposit a cheque in an alternative name into a personal bank account (Australia)
You don't have much choice other than to open an account in your business name, then do a money transfer, as @DJClayworth says.  You will not  without providing your name and street address and possibly other information that you may consider to be of a private nature. This is due to laws about fraud, money laundering and consumer protection. I'm not saying that's what you have in mind! But without accountability of the sort provided by names and street addresses, banks would be facilitating crimes of many sorts, which is why regulatory agencies enforce disclosure requirements.