I’m a bit late to this thread as I was on vacation last week, but before going right for the name part, I think there are some misconceptions throughout this thread that are worth addressing because they factor into choosing a name.
Clarifications
The first is this “full stack” or “siloed” view of an application. That is, that “DOTswap” represents not only the protocol but any tooling or UIs that people use to interact with it. I think if Web3 in general is to succeed, we have to be diligent about separating protocol from tooling from UIs in our discussions. Web2 bundles them all together in a silo because they are forced to due to their built-in trust assumptions. The fact that they are separate in Web3 is our advantage. If we speak about these things all bundled together then we are failing to communicate our number one value proposition over Web2: That we don’t need to trust a service provider to use a digital service (protocol).
The second is that the the main motivation for the DEX is to bring liquidity to other parachains. This is more of a tertiary objective. The primary objective is to allow accurate conversion of small asset balances. This feature will remove a lot of security concerns that hamper UX (e.g. being strict about which assets are sufficient). The ability to swap small (i.e. transaction fee, existential deposit) balances greatly simplifies fee payment and secures the network from several attacks. The DEX is also meant to contribute to a better Treasury system that allows proposals in other assets besides DOT. The fact that this same protocol can also be useful to other parachains is an added benefit, but not its raison d’être.
Moving Forward
Now to make some progress…
Similar to how Statemint is likely getting rebranded to “Asset hub”, I feel it would be best if we downplay this DEX as much as possible, make it feel like the infrastructure that it’s intended to be.
I’ve been frontrun 
. This is another forum thread I’ve wanted to start. I’ll write that shortly, but for now, yes, in my opinion we should rename Statemint to Polkadot Asset Hub. In brief, I think system parachains should have more neutral/functional naming to emphasize that they are in fact just sub-protocols of the Polkadot protocol.
Taking these into consideration, I can see where Dan is coming from. I think what Dan is saying is that DOTswap sounds like an end-user application. But DOTswap is actually a protocol, and we want to attract lots of tooling and UI developers to work with it, so we should choose a name that’s more indicative of that.
From the protocol’s point of view, the “swap” functionality should rarely even be seen by the user. The user stories can be things like, “Pay your transaction fees in any asset.” The wallet of course needs to know how to construct the SignedExtension with correct instructions, but the user doesn’t need to know what’s actually happening with that asset.
When I hear “DEX”, I think “protocol”. But it’s apparent that a lot of people think “application”. So perhaps it shouldn’t be called a DEX at all, something like “Pooled Asset Conversion {Protocol/Pallet}”. I think it’s great that the community got engaged in naming, so let’s try to keep that engagement, but also include other protocol developers and tooling/wallet developers in the discussion. No name has been “officially decided” (although yes DOTswap is being widely used now, but it’s still early). I think we can re-open this discussion and choose a name that does indicate that it’s a protocol and appeals to its target audience: tooling, UI, and parachain developers.