Hi Kenneth,
One business registration is fine, you can run as many online business's through that as you like. With an online store, your brand is really your domain name, not so much your business name. Your business name is more for taxation purposes these days, the domain name of your e-commerce sites is what you need to focus on marketing.
That said, don't confuse your tax records between the different sites, keep the records all separate.
Cheers