IMHO, Not really required if staying on the same frequency as the original receiving controller(s) will be fully aware of your situation. If you do get transferred to another frequency it's a good idea just to confirm that all the normal/abnormal internal (ATC to ATC) coordination has occurred; sometimes the actual message gets lost in the conversations and if it's a quick change after the event no coordination may have occurred or at least may not be fully complete.
And as mentioned above it's a great situational awareness tool for others on the frequency.