Page from a manuscript from Al-Andalus,
12 cent. Sura 15 : Al-Hijr.
Thicker letters in Kufic calligraphy
Source: Wikipedia Commons
All Western European, and eventually, Cyrillic alphabets derive from the early alphabets of the Middle East. For generations, archaeologists have dealt with Egyptian hieroglyphs and cuneiform writing, as well as those ancient alphabets that led to Hebrew and Arabic scripts.
Modern Arabic in all its forms is derived from 6th century Arabic. The spread of Islam took this writing system to three continents in a very short time, and the written form of native alphabets in many areas changed, with the exception of writing systems preserved by religion, as in Hebrew and the Coptic language. Even the language of a nation as ancient and large as Persia, now Iran, is now written in a script derived from Arabic.
Transliteration from another alphabet is always problematic to some degree, even without differing dialects and writing styles. As with Greek, Russian, Bulgarian, etc., certain schools of thought developed over time, sometimes working toward strict transliteration (letter by letter), sometimes working towards transcription (sound by sound), sometimes both. But both Arabic and Hebrew skip vowels! So a "transliteration' becomes far more than just transferring letter sounds. Without the added vowels, many words are unpronounceable.
For example (my thanks to Richard Lammert for this), there is the transliterated word " Mḥmd". Should that be read "Muḥammad," "Mahomed," "Mohammed," or "Maḥmūd" (all possibilities without an indication of what vowels to use). Readers might also see that this is where the many possibilities arise: there were no vowels in the written text, so they had to go on what they heard someone say.
Another problem: languages also change. When Kemal Ataturk's regime changed Turkish writing from an Arabic script to the Roman alphabet in the early 20th century, they were careful to transcribe the exact sounds of each word, so each word read exactly as it was written. If you study Turkish now, you might feel as though they used all the possible mismatches in English as their model, as pronunciation no longer matches the way the word is spelled -- and it took less than a hundred years to change this significantly.
One problem with Middle Eastern names is that the same person may have many ones... and not just simple differences like Nicholas of Cusa and Cusanus. People take new names for themselves, or are known by honorific names that have no relation to their original names ... like calling Richard I of England "Lionheart" or those early kings of France as just "The Bald One" or "The Fat" without saying "Charles" first.
As for transcription, Arabic and the languages using Arabic writing have such diverse sounds that you can have radically different transcriptions for the same exact words. Some rely on a lot of diacritical marks to try to consistently represent a particular sound; others try to make it easier for Westerners by using more familiar constructions (e.g. in English transcriptions, using the sh sound by writing "sh" rather than an s with a diacritical mark (as we write "Shiva" and "Vishnu" for the Hindu gods rather than "Śiva" and "Vişņu", or using 'ch' for a Czech word which would be written "č " in the language itself). Some use different transcriptions for the same Arabic letter when pronounced differently, others try to use diacritical marks to indicate which sound to use.
LINUS uses the Library of Congress headings as its search vocabulary; librarian-catalogers spend a lot of time and energy creating cross-references within the catalog to make your searching easier. Try using the preferred form of the name you find in LINUS or LINK+ as your first choice in searching other databases, though some of the diacritical marks, hyphens, underscores, etc. may have to be altered database by database.