The city of Duncan, Oklahoma, within the corporate limits as now established or as hereafter established, shall continue to be a municipal body politic and corporate in perpetuity under the name of the "City of Duncan, Oklahoma". It shall succeed to and possess all the property rights, privileges, franchises, powers and immunities now belonging to the corporation known as the city of Duncan, Oklahoma; and shall be liable for all debts and other obligations for which the corporation is now legally bound.