Why does Luke Danes' ダイナー, 食堂 have a sign that says Williams Hardware if it was his father's store? Wouldn't they have the same last name? Was this ever explained in the show?

i think it says William´s Hardware. and his dad was named William? but that´s just my guess, that´s how i always understood it :)

Like the person above me 発言しました it's William's not to be confused with Williams. Implying that the store is owned によって William. So his name was William Danes.

Yea his fathers name was William it was his hard where shop. The upstarts where look lives was his office .... Like gas 発言しました in the 表示する that someone was never supposed to live there hence it being so small :)

William was is dad's first name