An old Department of Fish and Game booklet (Marine Baits of California by Charles H. Turner and Jeremy C. Sexsmith) simply calls the moss "green sea moss" and uses the generic Enteromorpha spp. as the scientific name (thus including several different species).
According to their description, "green sea moss is a low-growing plant, almost grasslike in appearance. It forms a tick green mat, encrusting almost any substrate in shallow intertidal pools, on exposed rocks and pilings, and in shallow quiet bays and estuaries...The plants are from 1 to 15 inches long, depending on the species and local growth conditions. Some species, particularly bay forms, die or otherwise deteriorate n the winter."
The moss is certainly one of the top opaleye baits at Catalina and is perhaps the favorite bait used by the "professional" (or at least "semi-pro") Korean fishermen who travel to the Cabrillo Mole to fill their coolers with opaleye. I've heard some anglers call it "opaleye moss" and most get it off the rocks at different jetties from San Diego to Los Angeles. Some small bays (i.e., Mission Bay) and lagoons (i.e., Carlsbad) are also places where it's found — generally on the bottom. I've been told it's available at some bait shops in the Los Angeles area but not sure which ones. I think, but I could be wrong, that I've occasionally seen it at "Big Fish B&T" in Seal Beach.