Are you staying in the marital home where the utilities are, or is he?
What you may find is that some utilities will not take someone's name off the bill unless the person to be removed agrees. In my opinion the person who is moving out should always agree to have their name taken off. Otherwise they are setting themselves up to be liable for a bill they have no control over but where they are legally responsible to pay.
You may also find that some utilities want to charge you a FEE to change the names on the account. You can try to fight it by asking to speak to a supervisor.
If he is staying in the marital home and you are moving out, then you want your name off the bills ASAP. You don't want him running up charges where you have no control, but leaving you potentially liable.
For example he could decide to order up all kinds of extra cable services via On Demand and you have no say in it. If your name is still on that bill, it could hurt your credit rating if he stops paying.