Same designation for two persons is not a problem as such. For example, in the hotel industry, there are Banquet Managers. For convenience, they are given designation as Banquet Manager-1 and Banquet Manager-2 etc. They can have same reporting authority. In courier or logistic companies, there are many sales managers. However, each one has different sales responsibility like cargo sale, retail sale etc. Therefore, notwithstanding sameness in their designation, their area of responsibility should be different. There should not be overlap in any way.
From India, Bangalore
As Dinesh Sir has already enlighten you. Rights and duties, Work preferences reporting and authority should be properly delegated. Also many company's have GM for Every department (Viz GM HR, GM Finance, Etc) . As there is no point in hiring two authorities for the same work.
From India, Pune
As explained by seniors there is nothing wrong in having two General Managers, however their work areas may get assigned so that they are not interfering with each other's work. You may have proper JD or geographical area assigned to remove any doubt. In case there is any statutory obligations to be discharged by them on behalf of employer, say as a manager under the Factories Act or some other legal provisions, then you may have to specify that in their work guidelines.
From India, Mumbai