WARNING: PEOPLE NAMED EVE ARE PROHIBITED FROM INSTALLING THIS APP!
When teaching encryption / cryptography, it is common to use a story about sending messages from Alice to Bob (Party "A" and Party "B" respectively). Cueball claims to have created a texting app that only allows for this one thing. It does not, however, allow "Bob" to reply, making the usefulness of the app questionable at best. It is unclear how it enforces the name restriction, but it is possible that the app figures out the name of the phone's owner. The title text mentions Eve, who in the typical story represents an "eavesdropper", someone who attempts to intercept the messages between Alice and Bob. The fact that persons named Eve are 'forbidden' from installing the app suggests that it might not actually be as secure as Cueball advertises -- it may be that he naively thinks that it's just the name that makes the eavesdropper, and that by excluding all Eves, Alice's messages to Bob will remain private. It is not clear which phones will support this app, but it appears to be perfectly suited for the xkcd Phones.
The comics 177: Alice and Bob and 1323: Protocol are also about Alice and Bob.
Even if the assumption that you could divine people's roles and motives from their names were correct, if the names of the users don't need to be verified, it seems possible for a bad actor to circumvent the security features of the app by simply lying about their name. Genuine users could also undermine the security with double installations and a complete mess of a contact list in which everyone's names are somehow identified as "Alice" or "Bob", in order to increase its utility to them. Also, it would appear that "Bob" needn't be the commonly used name of the message receiver, in this scenario – it could also be a diminutive of what he is actually known by. Thus a user might claim to be "Bob" whichever his given name is.
This may be related to the announcement that Signal would be discontinuing support for SMS/MMS messages.