The Rosh (Gittin 4:7) writes that when comes to writing a bill of divorce (Get), the name that is used for to call up the husband to he receives an Aliyah should be what is included in the Get. Therefore, it is clear that the custom of calling up on Oleh by his name is an ancient custom. Interestingly, the Gemara (Berachot 55a) says that one of the things that shorten one’s life is being called up to the Torah and refusing.
The HIDA (Haim Sha’al, vol. I, § 13), on the other hand, says that the custom in Jerusalem was that one’s name would not be called out loud. Rather, the Shamash (sexton of the synagogue) would call up the Oleh in a more indirect manner, so as to prevent the possibility of one refusing to go up to the Torah and risking shortening one’s life. The Ben Ish Hai (Rav Pe’alim, vol. II, Orah Haim, § 16) writes that this is the custom as well. In Egypt, plaques would be distributed with the number of the Aliyah so that one’s name would not have to be called.
Nevertheless, the Moroccan custom is to publicly call out the name of the Oleh, which the Shamash precede by saying “Ya’amod HaShem Hatov…” (lit. “may the good name…rise”).. Rabbi Meir Elazar Attia (MiShulhan Avotenu, Sha’ar 1, pg. 84) writes that unlike some communities in which one is called by one’s name and one’s father’s name (eg. Moshe ben Avraham), the Moroccan custom is to include one’s last name as well (eg. either Moshe ben Avraham Bitton, or simply Moshe Bitton). Rabbi Yehuda Ayash (Ze Hashulhan) writes that in Algeria the custom was to use one’s name and father’s name on Shabbat, but on weekdays, one would simply be called up using “Ya’amod HaShem Hatov” to conform with the HIDA’s opinion.
It is written (Orhot Rabenu) that Rabbi Ya’akov Kanievsky (the Steipler) was insistant about being called up to the Torah by his name. Furthermore, Rabbi Israel Yehoshua Trunk (Yeshuot Malko, §12), Rabbi Itzhak Yehuda Schmelkes (Bet Itzhak, §20-21) and Rabbi Eliezer Waldenberg (Tzitz Eliezer, vol. 17. §16) are all adamant that one should be called up to the Torah by one’s name.
Summary: The Moroccan custom is that an Oleh is publicly called up to the Torah sing one’s name and last name.