Going to be hard I suspect. When you see equipment with no brand it tends to be that junk that you find being sold on the direct from china things like alibabA. You find lots of this stuff on ebay and amazon. Anyone who has money can start their own business. You just order xxx unit they put your brand name on them and ship them directly to a amazon warehouse from china. All the person does is write the sales ads they generally have no ability to provide any kind of tech support or many times do not have any understanding of what they are actually selling.
In general the reason these units are cheap is you get no tech support of any kind.
If you search google images you will see a massive number of different brands of devices that all look like your photo.
You might be able to get lucky and find some manufacture that has firmware images but you never really know if the units are exactly the same internally or if they will work. If you can find a FCC id number on the box or in the documentation it can help because you then can find the cpu and wifi chipset it uses and maybe find a software image. Note a lot of the junk shipped directly from china is illegal stuff that does not have official fcc approval. They tend to be grey market copies of devices that do have approval so they function they are just not legal.
This is why you spend the extra $10 or whatever to buy at least some more common brand name. TPlink tends to have good support and fairly low prices. Companies like asus can get away with charging a premium because their customer service is very good.