According to the Jerusalem Post (Sunday, May 11, 1997), "Zionists... chose last names that emphasized the quality of strength, including Even (stone), Sela (rock), Gazit (rock), Shaham (granite), Peled (steel), Tamir (tall) and Amir (treetop)..."
The persian theory also holds some water. Shaham is quoted as a boy's Parsi name (http://www.avesta.org/znames.htm). Although no etymology is provided, I suspect the name could be related with Shah ("king").
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