This 600-foot-long street, which runs from Western to 2nd Avenues a block south of Bay Street, was given that name by William Nathaniel Bell in 1881. In his plat, the large lot between Bay (then Grant) and Lake (now Broad) Streets west of Western Avenue (then West Street) was shown as occupied by the Eagle Manufacturing Co. On this 1884 Sanborn map, though, “Seattle Barrel M’f’y” appears instead. This historic survey says that the Seattle Barrel Manufacturing Company opened in 1880, but was located between Bell and Wall Streets, farther south.
At any rate, it would seem that Eagle Street was named after this Eagle Manufacturing Co., of which I could find no further trace; and that neither Eagle nor Seattle Barrel was there 30 years later, when the 1912 Baist atlas was produced, showing the land to be occupied by Union Oil Company of California (later known as Unocal).
Unocal — which, according to Historylink, had begun using the lot in 1910 — would continue to use it as a fuel depot and marketing terminal until 1975. Cleanup of the contaminated ground began in the 1980s, and the Seattle Art Museum purchased the site in 1999 with help from the Trust for Public Land. In 2007, the Olympic Sculpture Park opened, completing the area’s transformation from open space to industrial area to open space once again.
(Local historian Paul Dorpat points out that the cove that once existed here could be [though never was] called “Eagle Cove” — both for Eagle Street and for the fact that Alexander Calder’s Eagle sculpture now makes its home in the lower half of the park.)