You win this bet. College Library is not a building but a collection of books housed in a building, and that building has been called Helen C. White Hall since 1970 — a year before it opened. It has never been called Helen C. White Library (or at least not officially — I have no idea what your father calls it unofficially). Here’s a page from the October 1971 issue of the UW’s alumni magazine. As you read through, you’ll see “Helen C. White Hall” in multiple places. Feel free to wave this under Dad’s nose.
Helen C. White Hall is unusual on campus in that the university decided to construct a building on this site long before it knew what departments would live there. Almost all of the UW’s buildings were made for a certain purpose: to house science or humanities or engineering or medicine or whatnot. When the regents decided to put up a large building at 600 North Park Street in April 1964, they didn’t yet know what to put in said building. They just knew that they wanted to knock down Journalism Hall and Chemistry Hall (a decision made all the easier when a fire destroyed much of the journalism building in 1965). From 1964 until 1970, the project was simply called 600 North Park. In 1965, the UW decided that the undergraduate library would live there, and so would the School of Library and Information Studies (today’s iSchool). The rest of the occupants took a long time to decide.
The human Helen C. White (a.k.a. the lady in lavender, a.k.a. the Purple Goddess) was a longtime professor at the UW, and after she passed away in 1967, the regents chose to honor her by putting her name on the new building. It also added 4,000 of her personal books to the UW Libraries’ collection. And, of course, Helen C. now houses the department she taught in: English.