Dropbox's sign-in page shows a different app name or a warning. Is that right?
Short answer: Make sure the page is on dropbox.com. Dropbox's permission page names the connector Storage Studio uses, which may not say Storage Studio — that's expected. Approving lets Storage Studio on your Mac read and write your Dropbox for your transfers.
Check the address bar first: the page should be on dropbox.com. Dropbox shows its own permission page with the name of the connector Storage Studio uses to talk to Dropbox, which may not read "Storage Studio". That's expected, and you can approve it.
We don't publish the details of how the connection is built, but here's what it means for you: the permission lets Storage Studio, on your Mac, read and write your Dropbox for the transfers you set up. Your files go between your Mac and Dropbox directly. If anything on the page doesn't look like Dropbox's own site, close it and click Cancel in Storage Studio.