The 'major' name brand manufactures DO mark their motherboards with both their name and the model number.
Others, "may" place a sticker on the outside ISA slot.
For the most part, the unmarked motherboards are "OEM".
That does not necessarily mean that they were made for a name brand PC.
Many of the smaller motherboard brands do not have their own manufacturing plant. Instead, they use a "contract" manufacture to produce the motherboards for them.
In some cases, the contract manufacture operates as an OEM supplier. They build a "generic" motherboard and install a customer specific BIOS.
What I do with an unbranded motherboard, is take a close look at the chip-set.
I then look up the specifications of the chip-set and download the 'reference' drivers.
After setting up the motherboard with a supported CPU, watch the POST screen.
The BIOS string that shows up at the bottom of the screen is your "KEY" to who made the board.
With the BIOS string, you can use the tools at www.motherboards.org or www.wimsbios.com to track down the manufacture of the board.
I believe that WimsBIOS has a download that will display the information for you.
Still, you need to boot up the board to get this information.
Chas