This should work. The name of the data.frames created will be equal to the names within eqDataAll$SeismicRegion. Anyways, this practice of populating individual data.frames is not recommended. The more I work with R, the more I love/use list.
lapply(names(eqRegions), function(x) assign(x, eqRegions[[x]], envir = .GlobalEnv))
edit: Use list2env solution posted. Was not aware of list2env function.