Aruch Hashulchan EH 129:116 says one should not be called up to the torah with either your own or your fathers nickname like Zalman of 'Shlomo Zalman'. A nickname is a name, which is nothing more than a 'copy' of the original like Salamon or a shortened version of it. So why today are even rabbis called up to the Torah by a name including their nickname? Like the example given of Shlomo Zalman.
I think you might be mistaken in the premise of your question. If you were named something at your bris, it DOES become your name, even if it was originally a 'nickname' style of name. It's quite common nowadays that a person's 'Hebrew' name is based off another language (generally Yiddish, but not limited to it).
Rav Moshe has a Teshuva where someone asked if he could name their daughter after a relative who only had an 'English' name. He responded that yes, it was permitted, and the name becomes a 'Hebrew' name. He proved it from the Rambam's name: Rambam stands for Rabbi Moshe Ben Maimon. Maimon was definitely not an originally 'Hebrew' name, yet that was the name he was called. While originally it might not have been entirely appropriate (but certainly not forbidden) to give a child a not-classically-Jewish name, once the name is adopted into Judaism, there is no reason not to use it. (See Igros Moshe O.C. 4 Siman 66. Igros Moshe O.C. 5 Siman 10 also has a long discussion on names, which I haven't read through yet.)
I believe that the Aruch Hashulchan you brought in Siman 129 Sif 116 near the end where he mentions not to call people up to the Torah by nicknames is referring to nicknames that weren't given at the Bris. The Mevoh Hashe'arim you brought in the comment below seems to be the only place that mentions a Kinui given at birth, and while I'll concede his language seems to imply that Kinuyim are often given at birth, I still feel that most other places refer to Kinuyim that aren't given at birth.