I share your interest in good terminology; but it looks to me like it's probably far too late to get rid of 'The Singularity'.
I expect marketers to play along - but probably not scientists - or at least not serious ones in the relevant fields.
There are already a few exceptions, though. For example, Robin Hanson is apparently trying to rechristen the agricultural and industrial revolutions as being "singularites". However, I think most historians will go the other way around. The "industrial singularity" will just sound like crazy talk to most people.
If you have graphic design experience, check out the on-going logo design competition at 99designs for the Singularity Institute. There are still 6 days left to enter and be eligible to win the $295 prize if your design is selected. Tell your friends with graphic design experience too. There are very few submissions currently.
Note: This is a blind contest. Designers can only see their own entries. All designs will be revealed when the contest ends.
If you're interested at getting a peek at the designs, they will be online after the competition is over. This is standard practice in 99designs contests to prevent designers from contaminating each other and having all the designs drift in a certain direction.