I have a feeling I'm missing something big in what your saying so proceed with caution...
Assuming, you've installed symbiosis on bytemark machinery...
I think you're stuck with the six part
[machine].[group].[account].uk0.bigv.io format which, incidentally, is functional and aesthetically awesome. 
If you have created sites under
/srv then I'd suggest contacting support about dns authority for the domains before doing anything.
It's probably much easier to start a new image rather than move groups or change machine names under the Control Panel. You might even want to start over with a new account name...
Probably not -- I think you're talking about the machine name; by this stage, account and group names have already been assigned.
 On branding, we're told that "BigV" is bad and "cloud" is good -- the future is cloudy. I considered mounting a BigV preservation coup but I'd never get past bytemark's anonymous recruitment process. Yes, it's horribly unfair but they blatantly discriminate on ability. Putting aside the egregious attack on the masses, I'm going to enjoy *.uk0.bigv.io for as long as I can.