While I'm not an expert by any means, these names spread into the Western world as the Roman Empire became Christianized (as an aside we still retain some traditional Roman names too and Mark for example is actually just a short form of the Latin name Marcus). However we got the Latinized and later Anglicised forms whereas in the Middle East they retained the Aramaic and later Arabic forms (Miriam for Mary, Yeshuah for Joshua/Jesus/similar, and so forth). Hence the Latin and English variants became associated with Western Europe while the original names evolved in a different direction.

Biblical are still quite common throughout the Middle East! In my travels in the region, I've learned that Dawud (David), Ishaq (Isaac), Musa (Moses), Suleiman (Solomon), Ibrahim (Abraham), 'Isa (Jesus, or Joshua), Harun (Aaron), Yusuf (Joseph), Yaqub (Jacob), Yunus (Jonas), Maryam (Mary, Miriam), and several other Biblical names are common among Arabic-speaking Muslims; among Arabic-speaking Christians, names like Hanna (John), Butrus (Peter), Bulus (Paul), Jirjius (George), Mikhayil (Michael), and Tuma or Tanyus (Thomas) are also common. If you read enough histories of the region and sources from the era, you'll see all of these names appear many times. Wheeler Thackston's translation of the Lebanese historian Mikhayil Mishaqa's memoir of his 19th century life, which talks about many Christian and Muslim actors, includes many of these names!