The halachos of gitten can become complicated when more than one name is given.
Rama EH 129:1
כּוֹתְבִין שֵׁם הָאִישׁ וְהָאִשָּׁה, בַּגֵּט. וְאִם יֵשׁ לְאֶחָד מֵהֶם שְׁנֵי שֵׁמוֹת, כּוֹתְבִין שֵׁם שֶׁהֵם רְגִילִים בּוֹ וְיוֹדְעִים בּוֹ בְּיוֹתֵר, וְכוֹתְבִים: אִישׁ פְּלוֹנִי וְכָל שֵׁם שֶׁיֵּשׁ לוֹ גֵּרַשׁ אִשָּׁה פְּלוֹנִית וְכָל שֵׁם שֶׁיֵּשׁ לָהּ; וְאִם כָּתַב חֲנִיכָתוֹ וַחֲנִיכָתָהּ, כָּשֵׁר. הַגָּה: וְכָל שֶׁכֵּן אִם כָּתַב עִקַּר הַשֵּׁם לְבַד, דְּכָשֵׁר, וְלָכֵן אֵין לְהַקְפִּיד עַל הַכִּנּוּיִים כָּל כָּךְ. וְיֵשׁ אוֹמְרִים דְּאֵין לִכְתֹּב כָּל שׁוּם שֶׁיֵּשׁ לוֹ, אֶלָּא אִם יֵשׁ לוֹ שְׁנֵי שֵׁמוֹת יִכְתֹּב: פְּלוֹנִי דְּמִתְקְרֵי פְּלוֹנִי (רַבֵּנוּ תָּם וּבֵית יוֹסֵף בְּשֵׁם הָרַמְבַּ''ן וְהָרַשְׁבָּ''א), וְכֵן נוֹהֲגִין, וְאֵין לְשַׁנּוֹת. וַאֲפִלּוּ נִכְתַּב הַגֵּט אֵין לְגָרֵשׁ בּוֹ, אַף עַל פִּי שֶׁכָּתַב: כָּל שֵׁם, עַד שֶׁיִּכְתֹּב שְׁנֵי הַשֵּׁמוֹת (בְּקוּנְטְרֵס). לֹא כָּתַב אֶלָּא שֵׁם הָאֶחָד, אֲפִלּוּ הוּא שֵׁם הַטָּפֵל, וְגֵרַשׁ בּוֹ, כָּשֵׁר (טוּר):
They write the name of the man and the woman on the get (that is, the divorce document). If one of them has two names, then they write the name by which they are usually called and is most well known, and they write: man so-and-so, and all names that he has, divorced woman so-and-so and all names that she has. And, if [the scribe] wrote his or her surname, then [the get] is valid. Rem"a: And all the more so if he only wrote the main name, it is valid, and therefore one need not be precise for all the nicknames. And there are those that say not to write all the names that a person is called. Rather, if he has two names, then a person should write: so-and-so that is called such-and-such (Rabbeinu Tam, and the Beit Yosef in the name of the Ramba"n and the Rashb"a), and such is the practice and one should not change this. And even if [such] a get was written [i.e., without indicating the names], one should not divorce with it, even though it says: "every name [that this person has]" until [the scribe] writes both names (Kuntres). If [the scribe] only wrote one name, even if it is a secondary name, and [the husband] divorced with it, it is valid (Tur).