The term that refers to the inner struggle people go through in their effort to obey God in Islam is
Jihad al-Akbar (جهاد الأكبر), which translates to "the greater jihad".
While "jihad" is often associated with warfare, this is typically considered "Jihad al-Asghar" (the lesser jihad). Jihad al-Akbar focuses on the internal battle against one's own base desires, ego, and negative inclinations in order to live a life that is pleasing to Allah.
Therefore, Jihad al-Akbar is the most accurate and comprehensive term for the inner struggle in Islam.