The electoral roll is published annually (in December) but such things as name changes can be included in monthly updates which are issued each month except September, October and November. (This is the period during which the next electoral roll is being prepared, based upon the forms which are sent out in August or September). If your marriage occurs outside of these months, your local authority can supply you with the necessary form to have your change of name entered onto the roll.
As far as your voting rotes are concerned, it's not really that important to get the roll amended 'mid-term' because you're still entitled to vote using your maiden name. It's only for the purposes of organisations such as credit reference agencies for which you might need to bother making the change before the next annual form arrives.
Council Tax is charged against properties and not against individuals, so there's no need to notify the council about your name change. As long as they get their money, they won't care about the name on the cheque :-)
The only time that you would need to notify the council about a marriage would be if this resulted in one partner moving into the other partner's property (in which they had previously been the sole occupier). This would mean that the property would no longer qualify for the 25% single-occupier discount. That, of course, has nothing to do any name change (or indeed with the marital status of the couple living in the house).
Chris