This street is named for William Ashworth (1840–1906). According to the Haller Lake Community Club, Ashworth was born in England, emigrated to the United States in 1861, and came to Seattle in 1872.

Ashworth platted a town called Edgewater on the northern shore of Lake Union.… This area is now roughly the eastern part of Fremont and western portion of Wallingford.… Ashworth served as Edgewater’s only postmaster from 1889 until the area was annexed to Seattle two years later. As real estate development moved northward, so did the street bearing Ashworth’s name. Ashworth continued to live in Edgewater until his death in 1906.

Here is an article by local historian Paul Dorpat on Edgewater, on which it looks like I commented 13 years ago. And we learn both from the HLCC and Valarie Bunn of Wedgwood in Seattle History that the land on which berry farmer Ashworth’s home once stood is now the North Transfer Station (i.e., the city dump).

Today, Ashworth Avenue N begins at N 35th Street and goes ⅔ of a mile north to N 43rd Street. It resumes at N 55th Street and goes ¼ mile north to E Green Lake Way N, then begins again on the north side of the lake at Winona Avenue N and W Green Lake Drive N. From here, it goes another ⅔ of a mile to N 90th Street. Picking up again at N 92nd Street, it goes a further ⅞ of a mile to the Evergreen Washelli Cemetery at N 110th Street. It resumes one more time at N 120th Street and Stendall Drive N and goes 1¼ miles north to the city limits at N 145th Street, becoming a footpath for two short stretches west of Haller Lake. (As with many other North Seattle avenues, the name continues on into Shoreline; Ashworth Avenue N continues north of the city limits as far as N 200th Street, just south of the King–Snohomish county line at N 205th Street.)