Honda has made moves to protect the ADX name.
As first noted by Car and Driver, Honda filed trademark protection for the name with the U.S. Patent and Trademark Office on December 22, for use on automobiles and automotive structural parts.
While automakers often file trademarks for names they don't necessarily plan to use, there's a good chance we see ADX used on a vehicle, specifically a vehicle from Honda's Acura brand, in the not too distant future.
The “D” in the name suggests it's for a future Acura crossover, in similar fashion to the current MDX and RDX names. And we know that Acura is working on an electric crossover due to hit the market as a 2024 model. It's possible then that this new crossover will be called an ADX.
The electric crossover will be built by General Motors on the Ultium platform currently found in the 2022 GMC Hummer EV and 2023 Cadillac Lyriq, and will likely be similar in size to the MDX. Honda will launch a separate electric crossover for 2024, which will also be built by GM on the Ultium platform. Honda's crossover has been confirmed as the Prologue, and is expected to be smaller than the Acura crossover.
Another possibility, as suggested by Car and Driver, is an Acura subcompact crossover twinned with the latest generation of the Honda HR-V, though such a model, if it arrives, will likely be called a CDX, the name Acura used for a subcompact crossover twinned with the previous-generation HR-V and limited to the Chinese market.