Ortmann is most commonly found in Germany, including Prussia, Austria, and Russia. The distribution in Germany follows this pattern:
The earliest Ortmanns arrived in the US in the 1700's. Our ancestor Joseph Ortmann arrived in the early 1860's and served in the U.S. Navy in the Civil War.
Here's an interesting fact: One of the variations of Ortmann is "Erdmann," which in English translates to "Earthman." My maiden name was Ortmann. My (first) married name was Earthman. Go figure.