This street appears to originate in this 1871 plat made by Arthur A. Denny. Unlike with E North Street or Eastern Avenue N, no mystery here: originally named West Street, it was the first street west of Front Street (today’s 1st Avenue). Front Street ran along the waterfront, as its name implied, south of about Seneca Street, but north of there the Elliott Bay shoreline curved and the street grid didn’t curve with it (that would happen farther north, at Stewart Street). Hence West Street, which was changed to Western Avenue in 1895. (West Street would be extended farther south once they started filling in the tideflats; today, it begins at Yesler Way.)
Today, Western Avenue begins at Yesler Way and goes 1¾ miles northwest to Elliott Avenue W at 3rd Avenue W and W Thomas Street, having become Western Avenue W on crossing W Denny Way.