This is exactly the point indeed. What is shown here is simply what is pulled from the theming of the Nextcloud which people are looking at, so it might say anything, like “Jan’s cloud”, so it would say “Add to your Jan’s cloud”, which actually makes 0 sense indeed.
On the other hand, as you said, for a branded cloud, you probably don’t want it to say “Nextcloud” anywhere. Then again, the feature should possibly be disabled completely then as a label saying “Add to your [company name which you don’t work at]” does not make sense either.
So I’d say it indeed makes sense to call the label “Add to your Nextcloud” here, and offer a way to disable the entry. What do you think @szaimen @Andy?