The collection of scalar products is often called measurement. The collection of vectors (each being an atom) can be called measurement dictionaries or sensing dictionaries. This is not specific to random atoms.
In most of the literature I am familiar with (signal processing), these vectors are considered collectively as rows in a matrix, i.e.
$$\mathbf y = \mathbf E \mathbf x$$
where the $(M \times 1)$ vector $\mathbf y$ contains the measurements, i.e. the inner products of the Gaussian vectors $\mathbf e_i$ with $\mathbf x$. The sparse vector $\mathbf x$ is $(N \...