Now, for the elephant in the room:
If you ever get acquired, definitely call it a brexit internally. On that note I assume you got stuck with the name Brex _before_ all that happened, no?
Recently I've noticed that The Sun, Britain's foremost tabloid and an ardent supporter of aforementioned event, have started shortening the name to "Brex" in a few of their headlines. [1]
And now I'm also thinking of another company that ended up renaming themselves to avoid connotations with the name of the original event that inspired the name of the subsequent event that may or may not have inspired the name of this product. [2]
[1] https://twitter.com/TheSun/status/1046513253843718144
[2] https://qz.com/510040/grexit-the-unfortunately-named-softwar...