I kind of like just giving it the surname treatment. Band names are really kind of just about marketing and branding right? This is just three guys making music, they aren’t trying to be the next cool big thing. Does it even really need a name?
Surname treatment is a good marketing. These are familiar names.
Furthermore, this is already traditional in prog, fusion etc.
Bozzio Levin Stevens
Levin Minnemann Rudess
Emerson Lake & Palmer
etc
I dislike those names too, and I could care less about their music (ELP has a few decent tunes, but that's it for me) because those bands are one of those bands where it sounds good on paper, but the results are less than desired, to my tastes. It's like the lack of a creative band name = lack of creative music. Then you have a band like Vital Tech Tones, which is another super group that came up with a more creative name for themselves. Not so coincidentally, the music they made is way more interesting.
OK
It can be good marketing, I guess, if the names are big names outside of niche audiences.
Bozzio played with Zappa, Levin with Crimson, Gabriel, etc.. Rudess with DT among others, Stevens with Billy Idol, and on and on.
ELP originally had actual band names in mind, like Triton, Triumvirate, and Seahorse, but they went with ELP eventually, in part to take the focus off of Keith Emerson, who was the most well known of the three at the time of their formation, and to avoid being compared to The Nice (Keith's old band)
No one knows Neal, Nick, or Ross outside of a few specific online forums like this. The above mentioned musicians are quite well known around the world, in and out of prog circles.