I've been invited to review manuscripts for two journals in my field frequently. I noticed in the first couple of cases my supervisor was the associate editor which has selected me in the process, but for rest of them, I was assigned to the papers by other editors (not from our network).
So, I assumed that my name should be there somewhere in a list, such that the editors may choose me when they see a paper matches my keywords or my previous review results, etc.
Now, I want to state that in my CV and in a list separate from my ad-hoc review experiences, but I do not know what suitable key phrase I should use.
For instance, can I use the following?
Member of the review board for Journals X and Y
By the way, I work in the field of computer science.