"Algorithm" is derived from Al-Khwarizmi, but only because he translated the ancient Indian/Hindu "Sulba Sutras" texts into Persian, especially in his "Al Jabr" text.
"Sulba Sutra" literally means "method of problem solving". So the Sukna Sutras were all basically Algorithms - different ways to solve mathematical and scientific problems.
In fact, Al Khwarizmi himself borrowed the title of the original Indian/Hindu texts for his translations and he even acknowledged their Indian/Hindu origin. That's why the meaning of the full title of the Al Jabr book is "The Concise Book of Calculation by Restoration and Balancing" (because that's how algebraic equations are understood and solved).
This Al Jabr book (based on Hindu methods of problem solving and algebraic equations) got translated and understood by British and Europeans, so they simply named this new (new to them) branch of Mathematics as Algebra (derived from "Al Jabr").
SOURCE: the British scholar "Robert of Chester" who translated the Al Jabr book to Latin (during 1876-2956, published in 1915, under book title "Algebra of al-Khowarizmi") documented that the ancient Indians knew the algebraic equations BEFORE Al Khwarizmi. Not only that, Robert also confirmed the ancient Indians knew and used the Pythagorean triangle theorem before the time of Pythagoras.
You can check and read these evidences for yourself please. Sources are linked below.
Trivia: in 1974, IBM released an advertisement, in which it gave the credit of Algebra to most ancient Indian mathematicians.
In the advertisement, IBM had explained 'How India gave the world the logic of indeterminate equations' by naming three prominent historic mathematicians: Aryabhata, Bhaskara and Brahmagupta, who developed the concept of Algebra and gave meaning to something (Zero) which was termed to be meaningless before.
The IBm ad proclaimed:
"History owes a debt to three Indian mathematicians of 1500 years ago who developed Algebra to give meaning to the meaningless. Bhaskara, who originated the radical signs. Brahmagupta, who created the symbols. Aryabhata, who worked out the first equations. A search that continues today in new directions with newer tools, among them, a machine that helps man in more ways than any other inventions in history: the computer. We are proud that IBM introduced the manufacturing of computers and other data processing equipment in India, which are helping the nation meet the challenge of building a new tomorrow," reads the IBM advertisement.
IBM's advertisement also features an excerpt 'The Poetry of Algebra' from the book Indian Wisdom by Sir Monier Monier-Williams.
* Among the several contributions made by Aryabhata, he discovered the nine planets and found out the correct number of days in a year i.e. 365.
* Brahmagupta made one of the most significant contributions to mathematics when he introduced zero(0), which once stood for “nothing”.
* Bhāskara declared that any number divided by zero is infinity and that the sum of any number and infinity is also infinity.
* 2000 years before Fibinacci, the Indian scholar Pingala discovered and documented by 200 BC the series we today call as Fibonacci series. Pingala wrote the Chandahśāstra, a treatise on prosody — poetic meter. To study Sanskrit meters, he analyzed long and short syllables, generating combinations using what we would now call binary patterns and recursive enumeration.
And in doing so, he uncovered (and documented) the interesting series we today call as Fibonacci series.
1: https://en.wikipedia.org/wiki/Al-Khwarizmi#:~:text=His%20nam...