I guess it depends on context. If a bass player were to play along with you, would he or she play a B note or an A note as the "bottom" note?
If they'd play a B, then it's an A/B chord: An A chord with a B in the bass. Often, this sort of chord would function like a Bsus4 chord.
Now, on a standard-tuned uke, it's often not really practical for you to put the B as the lowest-pitched note, so you usually have to just cram it in there wherever you can, such as on the top. Still, if the
musical intent is for the B to be on the bottom, I'd still call it an A/B chord even if that's not how it winds up being voiced on the uke.
On the other hand, if our hypothetical bass player should play an A note, and your added B is really supposed to be "flavor" in the upper structure of the chord, then I'd call it an A(add2) or A(add9).
JJ
P.S. Technically, if you call it an A9, that implies a five-note chord that also includes the dominant 7th: A, C#, E,
G, and B.
An A(add2) is just an A triad with a B stuck in the middle: A, B, C#, and E.
An A(add9) is an A triad with the B added in the upper octave: A, C#, E, and B.
But again, on the uke, it's often more practical to play an add2 and an add9 the same way. We just don't have the range to worry about putting notes in the "correct" octave.