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In this web posting by Charles Kent Smith, former president of the American Names Society, he claims the popularity of Omar as the name of Americans in the 19th century (as in Omar Bradley) is due to the popularity of poems like the Rubaiyat. They are named after the famed poet Omar Khayyam, much the same way the names Homer or Milton or Virgil came into common usage.
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Omar occurs also in the bible
The sons of Eliphaz: Teman, Omar, Zepho, Gatam and Kenaz.
These were the chiefs among Esau's descendants: The sons of Eliphaz the firstborn of Esau: Chiefs Teman, Omar, Zepho, Kenaz,
Chronicles 1:36 - same as Genesis 36:11
The sons of Eliphaz: Teman, Omar, Zepho, Gatam and Kenaz;