A Gemeterian name is a djinn's ancient name that gives another person complete control of the djinn in question. It binds the djinn and allows the person to command them at their will. This is why most people keep their given gemeterian name a secret and only tell it to those they completely trust.
In the first book, Akhenaten tried to exract this information from Nimrod when he was threatening the twins. Giving in, Nimrod told the evil pharaoh his gemetrian name. Fortunately the twins and the Seventy Lost Djinn of Akhenaten were able to stop him before he was able to use the full extents of this power.