As someone who works at a Bitcoin/Ethereum company, and has passionately followed Bitcoin since 2011, every time I hear "blockchain" as a proper noun a piece of me dies inside. It's like saying "This Is Your Company on Website."
[un]fortunately this is no longer the case in the blockchain/vc world, which is the main reason you don't really hear much about new blockchain/bitcoin (or some other crypto) companies popping up and getting funded.
These days the blockchain world revolves around large companies(or groups of companies) setting things up for internal consumption and consulting companies trying to get in on the action to help those large companies with the setup.
I dunno. To someone like me who is all up into Bitcoin but not too serious about it, it sounds okay. Faddish, but okay.
I think the crucial distinction is whether you're pointing at an approach versus some specific implementation. 'Blockchain', as I understand it, is a particular approach that isn't linked to some particular instance.
"Your company on website" doesn't work because there's really only one 'web'. "Your company on Facebook" does work, as does "Your company on SCRUM/NoSQL/AOL/Mobile/etc."
I'd prefer "on a blockchain", personally, but "on blockchain" doesn't strike me as too egregious.
Maybe you could say "This Is Your Company on Web", which could imply plenty of things made possible by web technologies, like remote, distributed teams and cheap cloud infrastructure.
