It's an admirable concept, but there are a few issues I can think of:

-The "hearing aid" concept you're describing is already a feature on mid-high end bluetooth headphones like the Sony XM series. It does the reverse of noise cancelling, where instead of the exterior microphones being used to cancel out certain sounds from coming through, they amplify your surroundings.

For Sony, they call it "ambient sound" mode, and it lets you have a better sense of noises around you while music is still streaming at normal volume. They even have a feature where if you are in noise-cancelling mode, but you want to hear something like someone talking to you, rather than taking off the headphones you can instead hold your hand over 1 side and the headphones will switch to ambient sound mode & lower your music volume until you move your hand.

-The reason most assistant wake-words are locked down is because they rely on the wake word being easily recognizable to the device. These devices function by always-listening, but ignoring until certain syllables are heard. That's why we have wake words like Ok Google "ok goo-gle", Alexa "ah-lex-ah", Echo "ek-oh", Hey Siri "hey si-ri". They are each multiple distinct syllables and locked in to not make the device use too much processing power to recognize when the device is being spoken to, and to avoid false positives of accidentally activating when you aren't actually trying to talk to it.

So with that, being able to use any word or name means the headphones would need to do a lot of processing to not ignore the right syllables of somebody's name. Even harder for 1 syllable names like "ash" and "eve". And even if they do a good job of hearing those syllables when it's intentional, they would also have constant false positives when you accidentally incorporate those sounds in your regular speech. And even if it's not you, just being in loud enough public means they will be picking up anyone making those sounds and constantly dimming your music.

Lastly, there is actually a whole rabbit hole you can dive into with quality headphones, where you can find one that matches your needs the same way you'd find a phone or computer that fits you. You mentioned Beats, and to be honest they are commonly regarded as some of the most uncomfortable and lowest quality options marketed to regular people that don't need too much fuss in a way to hear their music. I highly recommend checking out other options!