1. It is easier to make an airplane than to modify a ship into an airplane- Which means if you already have a well-established brand, it would probably be simpler to create a separate, even competing, brand and just retain ownership of both.
2. The public is not actually stupid- While claiming new and improved may work for a short time, if there is no actual change for the customers’ value, then the overall brand loses.
3. Do not confuse lack of choice with loyalty to a brand- Many have been the regulated monopolies that thought they were doing well until they were allowed a competitor. So, before you start declaring a new product from a brand they can trust, ensure they actually trust the brand. Otherwise, see tip 1.
4. Emphasize with the customer- If you do not know exactly why customers see value in the existing brand, changing to another name/logo will not have the desired effect. If it is escape from an image of the current brand that is desired, know what drives the negative perception or you will probably replicate it. See tip 2.