Bornholm rosewood desk.... who designed it?  

Børge Mogensen had NOTHING to do with Bornholm Møbelfabrik.
The confusion arose because the logo usually has a large "BM" on top of the shape of the island. (Perhaps your sticker had the letters as well in a ink that was not lightfast). Many people have wanted to take the BM as the 'signature' of the designer and connected it to the famous designer whose initials are "BM". And then of course the Internet amplified this nonsense.
And every time I say it is nonsense I can feel a hundreds of complaints groaning and whining that so many people on the Internet say it is true, so it must be true.
Bornholm Møbelfabrik made in-house designs.
Here is an old advert where you can see the "BM" logo and the name of the company spelled out beside it:

And here is logo I've most commonly seen for Bornholms Møbelfabrik. Note the shape behind the logo is an outline of Bornholm island. And the star on the right is the location of Nexø, where the factory was. (Look it up in a map and you will see what I mean):

Thanks, Leif! I did not think it was a Borge Mogensen design 😉
I suspected they were all in-house designs... thank you for clarifying!
Stacey

Found it 🙂
Johannes Sorth for Bornholm.

I would be very curious to see what you've found?