Is it a derivative of the original Bus Pirate in some way, or just reusing the name?
Both in a way. Bus Pirate, both the hardware and the software, is completely open source. It's not the same version, things are different, but it's largely inspired by it.
However, the entire implementation is new, it's not a copy
Then you should not use their name.
Maybe it could be called "Bus-caneer"?
Nothing there adresses the problem. No one should have to tell you why it's wrong to use someone elses (reconized earned) name, or how "prefixed by esp32" does not change anything. Do what you want but don't delude yourself that you're in the right.
Plus this assumes the reader knows the actual Bus Pirate doesn't use ESP32.
Not to mention, what if the original bus pirate developers wanted to support esp32? It's just wrong all around.
Tomorrow I'm going to make one based on pi pico, and I want to sell them. But I have 2 problems:
1 I suck at embedded code and electronics design so my product barely works. It isn't reliable, accurate, or safe for the device under test.
2 there are already a ton of cheap mcu logic analyser projects and products...
How can I get mine to be popular instantly despite those problems? I'll just use someone else's popular recognized and well-regarded name that they earned the hard way. I'll call it the "Flipper Bus Pirate". This is totally ok because "Flipper Bus Pirate" is not "Bus Pirate" and it's also not "Flipper Zero". I don't understand why you are yelling at me.
I generally agree, and also do in this particular case, but one could argue that bus pirate is so successful that it turned into a genericide (Kleenex, Hoover, Thermos, Zipper, …).