My wife and I are about to have a baby, as such my wife is applying for paid parental leave which is painfully done through the Centrelink system. We also got married in the intervening years between us being on Centrelink regularly and now, and she subsequently decided to take my last name after our marriage. This has caused a headache linking accounts in her MyGov account since the information doesn't match and the system refuses to move forward. We eventually found a solution after tearing our hair out. I thought I would leave it here for any other lost souls who need this guidance.
Unlink all your accounts! This will allow you to link your Centrelink account. Yes you will have to relink your other accounts if you wish but this is probably a small price to pay versus being on hold with Centrelink for an interminably long amount of time.