Do I need a V5C in my name to sell a car after a bereavement?
There is no need. You can sell the car using the original V5C in the deceased's name, thus avoiding the addition of another 'former keeper.'
If you have already updated the V5C to your name, that's not an issue. It is useful if you are going to tax and insure the vehicle before selling, depending on the circumstances.
Regardless of any updates to the V5C, you must always notify the DVLA that the registered keeper has passed away.