Is it permissible to shorten the name and surname from "Ahmad Ali Al-Haj Hussein" to "Ahmad Hussein" due to issues with official documents?

There is no harm in changing one's name by associating oneself with one's grandfather or family. This is supported by the Prophet's — peace and blessings be upon him — attribution to his grandfather Abd al-Muttalib, as he said on the Day of Hunayn: "I am the Prophet, there is no lie; I am the son of Abd al-Muttalib." Al-Bukhari titled a chapter on this: "Chapter: One who attributes himself to his forefathers in Islam and in the pre-Islamic era (Jahiliyyah)."