It is interesting that you raise this, because we at I2P have been thinking the same thing. We discussed the issue of I2P terminology at 31C3 and decided that after 12 years of Tor/I2P coexistence, Tor had the upper hand with regard to commonplace terminology.
In our next release, we are changing most of our user-visible tunnel-related terms (I2P destination, tunnel, eepsite etc.) to instead use "Hidden services" in some way [0], to draw parallels to Tor hidden services - because as far as an end user is concerned, they do "pretty much" the same thing. And as far as we could tell, "hidden services" is now considered "too generic" for Tor [1], so it made sense to use it generically. Tags are now frozen for the 0.9.18 release, but we are still open to further discussion about terminology.
Ha, it seems kind of ironic that I2P would adopt “hidden services” just as people in Tor are talking about moving away from it. I would think that the same arguments against using those terms in Tor would apply to I2P (namely, it’s scary-sounding, and it’s general). In fact, *I* thought “onionsite” was a good term for the same reasons that I think that “eepsite” is good (namely, it doesn’t have negative connotations, and it’s specific to the technology).
I have heard someone (forget who) propose that 'Dark Web' be dropped in favour of CipherSpace which could include all of these privacy perserving protocols, leaving terms like "OnionSpace" for Tor, "I2PSpace/EEPSpace" for I2P etc.
I am certainly in favor of this kind of collaborative approach. It's hard enough already trying to make this stuff understandable to end users (usability and UX of the tools themselves aside), without having multiple kinda-similar-but-not tools trying to do so in different ways. A "united concept front" would benefit tools _and_ users.
There was a recent discussion among some Tor people where the “Private Web” was recommended as a good general replacement for the “Dark Web”. Perhaps the “Private Net” could also replace the “Dark Net” if you don’t want to limit yourself to the Web. “CipherSpace” didn’t come up as an option, but I have to say that I don’t really care for it. It sounds overly technical and also collides with the use of “cipherspace” used in cryptography to denote the set of messages that constitute valid ciphertext. That’s just my opinion, though!
Best, Aaron