Updated in 2017: after much discussion, we’ve opted to change the name on this entity to Rubus spectabilis Double-Flowered Group from its previous name of Rubus spectabilis ‘Olympic Double’ (and, prior to that, Rubus spectabilis ‘Flore Pleno’, a name often used to denote double-flowering forms of plants).
Our rationale? There are at least three known double-flowered salmonberries in written / oral records: one from Washington’s Olympic Peninsula, one from the mountains north of Vancouver, BC (encountered in the early 20th century by Phyllis Munday–this is almost certainly the source plant for the above image, and known for many years as ‘Flore Pleno’), and one from Vancouver Island somewhere in the Cowichan Valley area.
Without doing a side-by-side examination of all three, it is first safest to deem all of these as part of a double-flowered group to begin with. The Vancouver-area clone was given the name ‘Flore Pleno’, but the question then becomes whether that name was given after 1959 (in which case it is invalid due to being a Latinized cultivar name, according to the International Code of Nomenclature for Cultivated Plants). The earliest record I can find is this 1977 photograph labeled as such, so unless an earlier record can be found, it reverts to being unnamed (and hence Rubus spectabilis Double-Flowered Group).
As Rodger Whitlock explains in the comments section below, the Washington entity was first listed in a catalogue as Rubus spectabilis ‘Olympic’, not ‘Olympic Double’, so that is the name that should take preference, i.e., Rubus spectabilis ‘Olympic’ (Double-Flowered Group).
Lastly, it is uncertain whether the Cowichan Valley plant was ever propagated for commerce (though it may be in a few gardens!). This one should also be identified as Rubus spectabilis Double-Flowered Group.