Seedlings appear in watered locations here in the Seattle area also, as well as among rocks in walls. The parent tree will be somewhere near you, or the seed came home with another plant or other material you have put there.
Common name that has been stated twice on this thread already is probably the most prevalent. Tree has also been called Royal Paulownia, Blue Catalpa, Purple Catalpa, Foxglove Tree, Princess Tree and Cotton Tree. With internet searches and plant books with descriptions organized by botanical names, you will want to look using the botanical name. Common names can bring up all kinds of unrelated subjects, it is the botanical name that is more useful - that is why scientific naming system was invented.