Only one name will ever appear on your bill, however you can add your partner as an authorised contact person so that they can contact AGL on your behalf. You can find out more here: How do I add an authorised person to My Account?
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We can only set up accounts with 1 account holder which will also be a requirement to receiving concession rebates. She'll need to sign up a new account in her name, this can be done on our website here.
Please also check our concessions page to check if the card she holds is eligible for rebates.