Yes both EE plans would need to be taken out in your partner's name and under their EE ID (same EE ID as the Broadband is under).
I believe this can be done through the EE App or Website and should link automatically if signed into the Broadband account.
Payments would come on a single separate Mobile bill, which you could set up to a different Bank account, but this would still need to be in your partner's name for credit checks etc.
You could set up a standing order with your bank to transfer this amount into their account each month if you didn't want them paying for everything.
Details on how to get started can be found here: https://ee.co.uk/ee-one
