The overall initiative is great, we always love to see more codebases, projects and such be branded as “ By Polkadot”.
As to what <something> should be, I think different opinions are valuable in their own context, and I am optimistic that the diverse comments here will help us come to a good conclusion.
Regardless of that conclusion though, I think “ By Polkadot” is already a great step forward, and much better than team building in the Polkadot tech stack without any mention of it. So I hope acknowledging this helps us converge to a decision sooner rather than later.
As to my personal “opinion”, If we are talking about anything that is technologically linked to the Polkadot relay chain, be it a Parachain, a DApp on a parachain, a (meme)coin on a DApp on Parachain and so on, I would stick to a simple “Secured by Polkadot”.
If it is a purely research, non-profit, non-parachain-based project (prototyping a new blockchain type with Polkadot-SDK), then “Funded by Polkadot”.