Sophronios

Records show that the name Sophronios was in use as early as the 5th century BC, which means that it is actually an ancient Greek name, not a late Greek one:

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• https://www.trismegistos.org/nam/detail.php?record=5908 (in English; click on "Attestations by century")
• Sophronios at the Lexicon of Greek Personal Names (LGPN): http://clas-lgpn2.classics.ox.ac.uk/cgi-bin/lgpn_search.cgi?namenoaccents=%CE%A3%CF%89%CF%86%CF%81%CE%BF%CE%BD%CE%B9%CE%BF%CF%82 (in English; features 9 results - the earliest record is dated to c. 411 BC)

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I will say that Sophronios was not as common in ancient Greek times as it apparently was in late Greek times, though. In the ancient Greek era, the name Sophron (obviously from the same root) was more common:

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• https://www.trismegistos.org/nam/detail.php?record=5959 (in English; click on "Attestations by century")
• Sophron at the Lexicon of Greek Personal Names (LGPN): http://clas-lgpn2.classics.ox.ac.uk/cgi-bin/lgpn_search.cgi?namenoaccents=%CE%A3%CF%89%CF%86%CF%81%CF%89%CE%BD (in English; features 74 results - the earliest two records are both dated to the 5th century BC)

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A known bearer of the latter name was the Greek writer Sophron of Syracuse, who flourished around 430 BC:

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• https://en.wikipedia.org/wiki/Sophron (in English)