When originally creating a Premium for Family Account, it asks you to create a 'core' account that your invitees will recognize. I wasnt paying attention and thought this initial information was my first invitee and put my wifes details in. I guess it isnt a big deal since the service is working as intended, but I am unable to find any options or account settings where I can change this information.
The Premium for Family invite email includes the name provided when the plan was initially set up, as you mention. Keep in mind that this is only visible in the invites sent and it shouldn't affect how the plan works, if you've entered the wrong name by mistake.
Currently, it's not possible to change this, however, if you thing this is something you'd like to see in the future, we'd recommend heading here and adding your +VOTE and feedback.
On another note, if you'd like more information on how the Ideas Exchange works, make sure to head here.
Hope this helps!
Help others find this answer and click "Accept as Solution".
If you appreciate an answer, maybe give it a Like.