Sure, a blockchain could hold a trademark, a DAO would probably be the best agent for that. Ethereum has many trademarks. The Foundation name, the terms Ethereum Switzerland, Ethereum Asia, the Foundation logo and all related names, logos, product and service names, designs and slogans are trademarks of the Foundation or its affiliates or licensors. You must not use such marks without the prior written permission of the Foundation. https://trademarks.justia.com/866/34/ethereum-86634529.html
Sure, a blockchain could hold a trademark, a DAO would probably be the best agent for that. Ethereum has many trademarks. The Foundation name, the terms Ethereum Switzerland, Ethereum Asia, the Foundation logo and all related names, logos, product and service names, designs and slogans are trademarks of the Foundation or its affiliates or licensors. You must not use such marks without the prior written permission of the Foundation.
https://trademarks.justia.com/866/34/ethereum-86634529.html
That's a "foundation" not a blockchain.
You're right, I don't think a blockchain actually can because it's just a computer code running on a bunch of nodes.