The Beth Din (Jewish religious court) has a religious scribe draw up a "get", or religious divorce document, which the husband hands the wife, thus divorcing her. The get is then handed back to the presiding rabbi, who defaces it so that it cannot be used agin. The couple are then issued a Divorce Certificate, along with a Beth Din statement restating the terms of the get (Maaseh Beth Din).
The get lists all names used by the parties, e.g. Peretz known as Perry, nicknamed Pez. The rules for drawing up the get are defined in the Jewish legal texts, and are very detailed.

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Note added at 1 hr (2014-10-19 02:42:23 GMT)
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The documents listed above apply, obviously, in Israel. Jewish divorces elsewhere require both a civil divorce decree and religious divorce proceedings.

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Note added at 7 hrs (2014-10-19 08:58:27 GMT)
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For Maaseh Bet Din, I use Res Judicata - this was the term I was given by an experienced legal translator, who dealt with notarized translations (which tend to require a very literal style).