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Does Acquia have differential access to the trademark based on Dries' ownership of both Acquia and the trademark? In practice, the most high profile private branding of Drupal products and services are mainly in Acquia: Drupal Gardens, Acquia Drupal.
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Be careful asking a question and then citing marginally evidence as if it proves an answer to the question...
The question is if they got those trademarks fairly. The evidence you cite next is that their brands are high profile. These two things are not really connected.
To try to actually answer the question, I don't believe Acquia has extra access to the trademark process. Having gone through the trademark process I can say that an external team of lawyers manages and adjudicates the process which keeps Dries at arms length from all decisions.
But even without an audit of the process of granting trademarks it's pretty obvious that "Drupal Gardens" is a name which meets the guidelines for a commercial use of the trademark since it doesn't imply the nature of the service. "Acquia Drupal" is probably covered under fair use since it truly is the Acquia version of something.
The "Drupal Association" prior to this year was an unofficial name used primarily to describe "Drupal Vzw" a Belgian non profit.
Drupalcon Inc. is a non-profit in the USA. They are both non-profits, just in different countries.
Neither has been merged/folded/acquired: much of the business undertaken by the Drupal Association moved from Europe to USA making Drupalcon Inc the main body doing business. There was a governance update to officially make Drupalcon Inc the main focus of governance/efforts to match what was coming to be in practice.
The link you included, https://association.drupal.org/node/1584, does indeed have more information but it doesn't say the things you've said in your comment.. ;)
It's internally referred to as "bluecheese" and it's not available for download. The standard practice adopted when the first theme was launched and reconfirmed in the redesign is that the current drupal.org theme is reserved for use on drupal.org in order to protect the brand.
The IP history of the previous theme makes it unlikely that it will be released, but it's unlikely anyone wanted it at this point anyway.