In Antiquity Algeria was known as the Numidia Kingdom and its people called Numidians.

Algeria - Introduction to World Cultures and Customs [ by Ashan Pushpakumara Perera]

Algeria means 'Alger area'. He was the man that founded & settled that area in the 5th century B.C. during the time of the prophet Malachi.  That's why so many areas there are named after him "Alger". He had been a captive in ancient Babylon & was freed when the Persians conquered the Babylonian empire. After being freed from captivity he journeyed back to Jerusalem & from there gathered many family members & people & left to settle the area you call Alger'ia. He was from the tribe of Dan, The House of Isaac, House of Israel, tribe of the ship builders.. Now you actually know where the name Alger'ia comes from.. He was my ancestor, I am one of his descendants.

Correction there is no country called western sahara it belongs to morrocco