No one country to 'officially' manage it is likely a big factor, as is the fact that Arabic has a sort of diglossia between Modern Standard Arabic and the "dialects" spoken in each country. For names in particular, they are sometimes transcribed in a more phonetic way, trying to capture how people actually pronounce them in, say, Libya or Morocco or Egypt; and other times are transcribed in a more structural/etymological way based on the spelling, following one of the schemes for transcribing the Arabic alphabet into English, which are usually based on Modern Standard Arabic.
Greek has a version of the same variation, despite not having modern-day diglossia and being mostly associated with one country, because of the ancient/modern relationship. For example, the large peninsula in southern Greece, Χαλκιδική, is spelled: Halkidiki, Halkithiki, Halkidhiki, Chalcidice, Chalcidiki, Khalkidhiki, Chalkidike, etc. Some of the transliterations attempt to capture how it's pronounced in modern Greek (Halkidiki is close, but Khalkidhiki captures some of the nuance better if you know what the 'kh' and 'dh' sounds are supposed to be), others try to transcribe the Greek alphabet using one of the standard schemes for either ancient or modern Greek (Chalcidice is the classic transliteration), and others do some mixture.
People tend to have strong opinions as well; classicists and etymologists don't like the obscuring of spelling that the phonetic transcriptions produce, but Greeks wince at people pronouncing Halkidiki as if it started with the English word "chalk" and ended with "dice". I imagine many Arabs similarly favor the more phonetic spellings for their names.