Typically, if the utilities are included in the rent as per the lease then they would remain in the landlord's name. If the tenant is responsible for the utilities as per the lease, then they would typically be placed into the tenants name. Pretty much there is no standard procedure as you need to simply refer to the lease and what ever is worked out with the landlord.
Hope that helps.
The answer below is correct. You can always ask that the landlord cover the heat, most local apartment complexes pay for heat. Usually the sewer bill stays in the landlord's name but then they copy the bill and charge to you . Good luck on your rental. BTW- for the price of a rental and the initial security deposit, you can get a USDA 100% home loan and BUY in near by Lacey or Manchester. Let me know if you would like more information.