This street — originally known as Lincoln when platted in 1875 by Rezin and Margaret Pontius (see Fairview Avenue N) — took the Pontius name as part of the Great Renaming of 1895, when the original Pontius (platted in 1880 by Margaret) became Melrose.
Pontius Avenue N runs ⅓ of a mile from John Street north to just past Mercer Street, where it dead-ends at the Interstate 5–Mercer Street interchange (originally constructed in 1962–1963 as part of the planned Bay Freeway, which was cancelled 10 years later with little more progress having been made. Its original northern end was Roy Street.) Pontius originally began one block further south, at Denny Way, but this portion was vacated as part of the construction of the Denny Substation.*
* Or was it? The clerk file indicates the vacation was granted, but I can find no related ordinance, and the King County Parcel Viewer and quarter section map show the Pontius right-of-way still existing between Denny and John. Something for me to look into… sometime.