Always a pleasure to welcome new members, and always glad to help where I can. Also happy, your daughter has a loving and supportive family, sadly it’s not always the case (I had to literally save my own godson’s life, so I know more than I would want to).
So, yes, create the account under your name, add a matching PayPal account, and don’t forget to fill out the W-8BEN form. This one is imperative to get paid and to take advantage of tax treaties between the US and the UK. Otherwise, Zazzle can not pay you and also has to keep 30% of your royalties for US tax purposes.
You can download the W-8BEN form directly from the IRS official site, here’s the link: https://www.irs.gov/pub/irs-pdf/fw8ben.pdf .
And here’s the link to the newest 2001 tax treaty document between the UK and the US, here you find the tax rates and paragraphs info for the form: https://home.treasury.gov/system/files/131/Treaty-UK-7-24-2001.pdf
Checked for you, in your case, the part concerning Royalties is Article 12, Paragraph 1. In the section Part II/10 of the form fill in the fields as follows: Article/Paragraph: 12(1), Royalty Rate: 0 , type of income: Royalties for the use of artistic work , and in the additional conditions/explanation field add something like this (worked for me, most struggle in this part): Creation of artistic works (designs) sold on Zazzle online webstores on a range of goods.
In regard to the stores, your daughter can open as many under the same account as she likes. Just keep in mind to choose the name wisely, you can’t change it afterward. It’s always debated what is better, one large single store or different themed ones. There are pros and cons to both variants - more stores can help differentiate your audience/themes, but it may be harder to manage, plus you cannot move items from one store to another. One single store may get overwhelming with time and depending on your content, some themes/styles may not be appropriate for some audiences.
When she turns 18 you can contact Zazzle support to transfer the account to her.
Hope this extra info helped to get an easier start and to avoid mistakes.
Good luck and don’t hesitate to ask for help if you get stuck, we have a truly nice community here on Zazzle, both designers, and mods.
Greetings from Mt. Etna Volcano!