From Manning, Robb, GunDigest Book of CZ Firearms, 2017, page 11....
"The first thing to get out of the way is the fact that, despite the name, the 805 Bren has nothing to do with the original World War II era BREN made in collaboration between Brno of Czechoslovakia and Enfield of England (hence Br En) and based on CZ's ZB LK Vz26 series of light machine guns. That's a lot of letters, so to break it down, ZB is Zbrojovka Brno which means "arms factory in Brno." LK is Lehky Kulomet, or light machine gun. Vz is short for Vzor, which means model and is the Czech military designation, like the "M" is U.S. M9)."
Pages 10-25 in the above reference gives a lot of detail of how the 805 was developed, the competitions, acceptance and operation.
No further mention is made about exactly how the term Bren came to be associated with the series beginning with the 805.
The best guess is an "homage".
I highly recommend if you are into collecting CZs, pistols or rifles, this 286 page reference is a must-have.