If a company splits-off and a division is eliminated, with half of the staff eliminated and a new company formed, can the new company use the testimonials that were prepared for the former company and change the names of the individuals (now gone from company) to show another name?
(For example, "Sue was a rockstar", but Sue is no longer with the new company and the name is changed on the new company's website.)
There are a few different questions here.
One is a copyright question, another relates to moral rights, while a third relates to "fair trading".
The copyright question is this: has the new company been granted a licence by the copyright owners (or controllers) to adapt and amend the testimonials? If not, then the adaptation and publication of the testimonials by the new company is likely to amount to an infringement of copyright.
The moral rights question concerns a special right to object to false attributions. See:
Depending upon all the circumstances, however, the fair trading question may be most important. If you are dealing with consumers (vs business customers), the fair trading question arises primarily under the Consumer Protection from Unfair Trading Regulations 2008. See Regulation 5 for a beautifully convoluted definition of "misleading action":
Note, in particular, Regulation 5(4)(f).
As always, I'm assuming English law applies.