Kings would be differentiated by a given surname of some sort. How that was granted differs between examples. So for example, you wouldn't see Antiochos I and Antiochos II or Ptolemaios I and Ptolemaios III; instead you would see Antiochos Soter and Antiochos Theos or Ptolemaios Soter and Ptolemaios Euergetes.
It's a bit more complicated than that, but that is the simple rundown of it.
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