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Last name origins & meanings:

1. Polish, Slovak, Slovenian (Prekmurje, i.e. easternmost Slovenia), and Serbian: from the common Slavic personal name Bogdan, bohdan composed of the elements Bog ‘God’ + dan ‘gift’. This was not a Christian name sanctioned by the Orthodox Church, but was common as a familiar vernacular name, equivalent to Greek Theodōros ‘gift of God’ (see Theodore) or Theodōtos ‘given by God’. As an American surname, it may also be a shortened form of any of numerous other Slavic surnames formed from this personal name.
2. Hungarian (Bogdán): habitational name for someone from any of numerous places called Bogdány, in Abaúj, Pest, Szabolcs, and Veszprém counties, or in Máramaros, now in Romania.
3. Jewish (eastern Ashkenazic): habitational name from any of numerous places in Belarus and Poland called Bogdany.