The vertical axis by convention. A named direction rather than a thing.
The letter descends from Greek Υ (upsilon), borrowed a second time into the Latin alphabet specifically to spell Greek loanwords, which is why Roman grammarians called it "i Graeca" — the Greek i, the form that gives French i grec and Spanish i griega their names. Its use as a second algebraic unknown follows the same convention Descartes fixed for x in La Géométrie (1637): the alphabet's last letters marking what is not yet known.
A second axis, named the way a second unknown gets named once one is not enough — paired with x not because it is known, but so a second dimension can be spoken of at all.