Love the idea, and have an additional idea to go along with this.
Perhaps instead of a militia there just be two legions of republic soldiers. One of clones and one of non-clones. Contrary to popular belief the republic military wasn't entirely clones. As a matter of fact clones were small, only counting towards 5-6 million at the height and around 9 million at the end of the clone wars. There were meanwhile millions upon millions of volunteers that formed legions and auxiliaries in the Republic Army. Grand Army of the Republic /=/ Republic Army after all. The volunteer units eventually becoming the mainstay imperial army while the clones became the basis of the Stormtrooper Corps.
If we do go with the Militia, most Republic Militias or Auxiliaries would be known as Sentinal Divisions.