I have created a spinning ball with a logo on the front.
However the animation works diagonally instead of round the ‘equator’.
How do I align the ball so it spins around the vertical axis?
Do you mean that your ball is spinning the wrong direction or that it spins around another center like planets around the sun?
If you have animated it to spin a certain direction but it spins another then you should probably delete the keyframes, press Ctrl+A and apply the rotation of the object and then animate it again.
If the ball is spinning around “the sun” then select your ball and press Ctrl+Shift+Alt+C and set the origin of the object to your geometry. This will place the origin (or the pivot point) in the center of your geometry so that your object should spin around that point.