Pup
I would think any deal on baby will include the use of the name for a period of time much as is the case with regional, although the impact on regional may well be higher without the bmi in front of it,bmibaby or baby having dropped the bmi bit is a easier rebrand in my view.
Monarch and Rome DJ you could well be right and I have no doubt that some passenger will be reluctant to book with baby whilst there is uncertainty over it's future, but most don't read Pprune clearly there has been uncertainty over the future of baby for the last 3 years, but it hasn't stopped people booking with them ! Fortunately because of the state of the UK market it has moved to a late booking market and if this can be settled before the peak booking season after Christmas then I think it's impact will be limited.
Baby is web airline and needs only bmibaby.com to re route to another domain name is easy stuff supported by marketing spend
The problem is everyone assumes that it will be another airline that buys baby, I don't see that, why would Jet2 or any other player want the hassle of different pays scales, management structure, the TUPE stuff? when they could just put aircraft into EMA & BHX ?