I would imagine that you could buy the name of a RTF that has chosen to cease trading and inform the CAA of a change of address,
Neither a RTF nor an ATO can be transferred.
Any organisation providing training is well advised to do so as a Limited Company, simply to limit individual's liability should something go wrong. Operating as a sole trader would be foolish at best and is not relevant to any EASA definition. A non-complex ATO is based upon less that 20 fulltime staff; in the main, the average RTF comprises of only one or two people, none of whom are full-time or even paid staff, where management structure and most of the "corporate style" requirements are meaningless nonsense that generate more work than the training itself and render a small ATO unsustainable.