These drives are mostly Phison and Silicon Motion designs. The controller vendors provide a turnkey solution of controller+firmware+PCB layout and usually help hook you up with a contract manufacturer who's already producing the same drive for other brands. This business model means it takes essentially no engineering resources to start a new SSD brand—you just need to decide what the label is going to look like.
A lot of existing SSD brands have moved mostly or entirely to this model. The ones that still do non-trivial engineering in-house for at least some of their consumer SSDs are the vertically-integrated companies that make their own memory or controllers (Samsung, Intel, Micron, Toshiba, WD/SanDisk, SK Hynix) and a few of the larger OEMs ( eg. Lite-On/Plextor, ADATA) who still source controllers and NAND from several companies. You can find the same Phison drives being sold by Corsair, Kingston, MyDigitalSSD, Patriot, PNY, Team, Zotac; likewise for Silicon Motion drives sold by ADATA, HP, Mushkin, and others. Using a Phison or Silicon Motion controller doesn't mean a drive is definitely identical to the controller vendor's reference design, but the degree of customization usually doesn't go much beyond cosmetics.
I've been seeing an increase in vendors who try to pretend the controllers are their own. Toshiba/OCZ Trion series SATA SSDs have been doing this forever with Phison S10 and now S11 controllers; Intel's been claiming to have customized Silicon Motion's NVMe controllers at the hardware level; HP puts their own logo on SMI controllers. I don't mind this too much when there is at least significant firmware customization, but for some brands it's really obvious that they don't have enough volume to justify even that much investment.