Is it permissible, in Sharia, for a Muslim to keep his Western name that he was compelled to adopt in non-Islamic countries in order to enter his country and see his family, considering his repeated attempts to change it, and the resulting problems in dealing with some Muslims?

The default ruling for changing names is permissibility, to a good or better name. It may even be obligatory if the name contradicts Islamic creed, such as "Abd al-Masih" (Servant of the Messiah). As for changing an Islamic name to a non-Islamic one, it falls under imitating non-Muslims, which is prohibited. However, if there is a necessity, such as entering your country, then the warning does not apply to you, though there is sin involved unless necessity truly compels it. What is obligatory upon you is to repent and strive to officially reclaim your Islamic name, or at least use it in your dealings with people.