Do I need a V5C in my name after a bereavement?

No – you can sell the car with the original V5C in the deceased's name, avoiding the addition of another 'former keeper' if you don't intend to drive the car before it is sold. However, if you have already put the V5C in your name, it's not a problem.

If you do intend to drive the vehicle before selling, you will need to put the V5C in your name to tax and insure the vehicle. You can do can do that here. 

Always tell the DVLA that the registered keeper has died, regardless of V5C updates.

If you do keep the V5C in the name of the deceased, once you have sold the vehicle, you need to notify the DVLA of the sale which you can do here.