The Tar- in Tar-Ardamin's name is a royal prefix ('King' in this case), and Arda is surely a reference to Arda, the world. The ending -min is less certain, but usually refers to prominent, outstanding people or things. It is difficult to combine these elements into a form that makes clear sense in English, but Tar-Ardamin's name seems to be communicating something like 'foremost of the kings of the world'.