How did algebra get its name?

Answer 1

The earliest known use of algebra was as far back as the ancient Egyptians, but the earliest written work on the subject was by and Alexandrian named Diophantus in AD 350. It had been used for many years afterwards but was not named until about AD 820. A certain Arab named Al-Khwarizmi wrote a book entitled Al-jebr wa'lmuqābala from which algebra received its name. Reference: E. F. Bozman, M. A. (1967) Everyman's Encyclopaedia, Volume 1 [A-BA], London: J. M. Dent and Sons Ltd

Answer 2

It was named after the title of one of Al Khwarizmi's books called Al Jabr, which means the addition of one thing to another.
The word "algebra" is named after the Arabic word "al-jabr" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by the Persian mathematician Muhammad ibn Mūsā al-khwārizmī in 820. The word Al-Jabr means "reunion". The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra" but debate now exists as to whether or not Al-Khwarizmi should take that title.