The time AH spends on Even HaEzer 129--as did SA and others—show the significance halachah attaches to the correct writing of the get, I think for fear of an invalidating error, which translates into a woman thinking she is divorced when she is not. Should she remarry and have children, they would be mamzerim, a status that can never be removed and is handed down in perpetuity (unavoidably, if the mamzer is a girl).
[As always, where we focus our worries and care shapes other choices, too, ripples we should make sure to stop and notice, to better calibrate our decisions.]
Nicknames Aren’t All the Same
In se’if fifty, AH summarizes SA in se’if fifteen, nicknames that stem from the real one (he has Chakin for Yitzchak, Arnin for Aharon) don’t need to be written, unless someone else in the vicinity also has that name. Where the shorter name is itself a name, like Chanan for Elchanan, we must write it (Elchanan who is called Chanan).
Where the nickname is related but not a form of the Hebrew name, we write de-mitkerei, who is called, while for a nickname with no connection to the original (Watermelon, because she likes watermelon), we write ha-mechuneh, who is also named. SA had included Leon for Yehudah as an example of a nickname directly connected to the real name, and Rema explains.s Leon means lion, and Ya’akov Avinu blessed Yehudah with the words gur aryeh Yehudah, so nicknames referring to a lion are seen as extending directly.
[Direct isn’t always direct.]
However, Rema reports the custom of his area, to limit de-mitkerei to Hebrew names, to introduce any non-Hebrew name with ha-mechuneh, regardless of how close it is to the original. He also thinks we should omit family names.
The Priority of Hebrew Names
Continuing his preference for Hebrew, Rema (presented to us by AH in se’if fifty-two) considered a man’s Hebrew name, the one by which he is called to the Torah, his main name, even if he has a more commonly used non-Hebrew name (Frank Jones would be written in a get as Ephraim Henoch de-mitkerei Frank). He ruled the same way for a woman, even though she is never called to the Torah, so her Hebrew name might be used only very rarely.
For other names almost never used, Rema said to write de-itkerei, who has been called, rather than de-mitkerei, who is called. In se’if sixty-one, AH pointed out that SA thought there had to be some people who used the woman’s Hebrew name, else it’s a shem she-nishtake’a, a name that has disappeared, and should not appear on the get at all.
