Brands are a mark of ownership so it follows that when this changes, it is time to visit the brand strategy.
Often the acquirer will impose their brand on the company acquired, sometimes without appropriate communication and therefore damaging consequences. Employees and customers are loyal to the original owner - if ownership changes it follows that there needs to be respect shown to the original brand. Replacing one brand with another without communication is discourteous and confusing. This doesn’t mean that the original brand needs to be over indulged either. Being decisive and communicating well is often the best policy. Some highly acquisitive companies like GE have developed this process into a fine art.
Sometimes companies will not only merge the business but will merge the brands themselves e.g. LloydsTSB, This is the least satisfactory solution as it is unclear who the true owner is - brand compromises are rarely the best solution.
Without new ownership, new product, or new position there is rarely a reason to dramatically change the brand. When ownership is consistent the brand needs only to be refreshed to keep pace with contemporary style and design. Shell, IBM, Barclays, 3M all have had many iterations in there lifetime. It is advisable to refresh the brand every five years.