BAM (Beam Anonymous Messenger) - It’s a good name, short and impactful. And it includes the brand name “Beam”.
Unfortunately it is already taken by the freshly released Beam Asset Minter (which, in terms of marketing impact, does not really deserve to have a particularly cool name). So a possibility would be to keep BAM for the messenger, and simply rename the Asset Minter.
For the later, any of the following could be used for its new name:
SAM (Secure Asset Minter) - Secure because it limits the max supply
CAM (Confidential Asset Miner) - Makes sense because CA = “Confidential Asset”, and thus CAM = “CA Minter”
BCAM (Beam Confidential Asset Minter) - Just because we like to add “Beam” everywhere!
As far as I understand, the messenger won’t be a standalone super cool and feature-rich app. We are not competing with Telegram or Signal here. We are talking about a very simple messenger that can be easily built on top of the SBBS (and maybe also the HTML/CSS/JS display capabilities) which are already included in the Beam Wallet.
Thus, I think that the name should not be too ambitious or too distant from Beam. It’s just yet another feature of Beam ecosystem.
As a consequence, I believe that simple names that include the word “Beam” make more sense (e.g. Beam Messenger, BAM, etc.).