Well, the wikipedia page for both Al-Khwarizmi and algebra both disagree with you, as does the wiki page for Geber, and, oh yeah, the journal of the history of mathematics: https://doi.org/10.1016/j.hm.2006.02.006

"It is well known that our word “algebra” derives ultimately from the Arabic al-jabr, which is part of the name al-jabr wa’l-muq¯abala given to the art of algebra in medieval times. Further, the individual words al-jabr and al-muq¯abala are associated with two steps in the simplification of equations. Al-jabr is the word used in conjunction with moving subtracted quantities to the other side of the equation, and al-muq¯abala is used to combine like terms on opposite sides of the equation."

I have additional notes, if the literal source on the history of math is insufficient to convince you of the history of math.