Some people seem to be a little paranoid about this:
There is no requirement to provide a name and address to get a Myki card.
You can buy a full fare Myki card from a vending machine. No details given, using cash or credit/debit/EFTPOS card to pay.
You can buy a full fare or concession Myki card from a station booking office or retail outlet, using cash or card to pay. No details given.
You can buy a full fare or concession Myki card online using a card to pay. Obviously they need your details to mail out the card. They then delete those details after the card has been sent. If you don’t trust them on this, use one of the above options.
People can choose to register their name and address to a Myki card. That means if the card is lost, it can be blocked and the balance transferred to a new card. It also means you can view the account online — however you can do online topups even with an anonymous card.
So if you’re concerned about your details and don’t want to give them to the Transport Ticketing Authority, you don’t have to.