The frequency is, as always, the number of cycles per second of the oscillations. It is related to the spatial wavelength by $f = \frac{c}{2 \pi} |\vec{k}|$, where $c$ is the speed of propagation of free waves in the medium and $$ \vec{k} = (k_x, k_y, k_z) = \left( \frac{2 \pi}{\lambda_x}, \frac{2 \pi}{\lambda_y}, \frac{2 \pi}{\lambda_z} \right). $$ and so $$ |\vec{k}| = 2 \pi \sqrt{ \lambda_x^{-2} + \lambda_y^{-2} + \lambda_z^{-2}}. $$ There are an infinite number of possible $\lambda_i$ for each direction, depending on the dimension of the box in that direction and the number of nodes & anti-nodes. Each one can, in principle, give rise to a different frequency.
Note that this relationship between frequency and wavelength is exactly the same as it would be for a free wave with the same wave vector $\vec{k}$. This is because a standing wave solution, such as a wave in a waveguide, can always be expressed as a sum of traveling waves that just happen to interfere at the boundaries of the waveguide. In the 3D case you need to have a sum of waves whose $\vec{k}$ vectors are of the form $\left( \pm \frac{2 \pi}{\lambda_x}, \pm \frac{2 \pi}{\lambda_y}, \pm \frac{2 \pi}{\lambda_z} \right)$; but all eight possibilities have the same magnitude $|\vec{k}|$ and so have the same frequency.