I've never heard "non-branded" used, so I'm tempted to say it's incorrect. I have heard "branded," though it is definitely used less than "brand-name" and "designer." It is less natural than the other two, but I don't know if it's considered incorrect. Sorry that doesn't actually answer your question. I hope this helps regardless.

Have you tried using google? Search for both, Google will autocorrect your search to the most common search and results. But, you have to use Google with English settings and not your native language. It's a faster way to get answers for questions like these.