Halakhah do Rodzaju 49:9

If the second name is derived from a Hebrew name, such as "Yehudah Leon," we write, "Yehudah, who is called Leon," and if it does not resemble the Hebrew name at all, he should write, "who is nicknamed." Rem"a: The explanation of his words is that "Leon" means lion, and Yehudah is called "the lion cub Yehudah" (Genesis 49:9). According to this, one should write, "Yehudah, who is called Leib." However, there are those who say that whenever both names are in Hebrew, we write, "who is called," and if one is in a foreign language, we write, "who is nicknamed" (Hagahot Maimoni 3, Sefer Mitsvot Katan, and Kol Bo). There is no difference whether it [the foreign name] is derived from the [Hebrew] name or not, and therefore we write, "Yehudah, who is nicknamed Leib" and all the like, and such is the practice in these countries. Any family name is not written at all, whether it is Hebrew or a foreign language (Seder Gittin), and such is the practice. One who has a Hebrew name by which he is called to read from the Torah, and who also has a name in a foreign language, we treat the Hebrew name as the main one, and regarding the second one we write, "who is called." The same applies to a woman--we treat the Hebrew name as the main one. There are those who say that one who has two names, if he is typically called by both and nonetheless one of them takes more priority, we write, "So-and-so, who calls himself so-and.-so." If he is not typically called by the second, we write, "who is called" (Seder Gittin). Any nickname which is a disgrace to the divorcer, we do not write it in the bill of divorce (D"A). Therefore, for an apostate who returned, we do not write, "and any other name by which he is known" (M"K). Any nickname by which he is not known alone, but rather he is called by [that nickname] together with the main name, there is no need to write that nickname (T"H #235). However, if the Cutheans call him by that nickname alone, even though Jews do not call him that, there are those who say that we do write, "and any other name," even though we do not write that in any other document, and so too regarding family names (ibid.). It seems to me that one should not write that nickname at all, as is the practice regarding family names.