The naming of the bachelor degree for engineering graduates actually varies from one university to another. In Canada, McGill U. and McMaster U. simply name it as B.Eng. (Bachelor of Engineering). Engineering students at U. of Toronto and U. of Waterloo will become a BASc (Bachelor of Applied Science). Queen's University prefers the name "Bachelor of Science in Engineering" as you mentioned. No matter what they call it, it's the same thing. And all unversities run Engineering and Science as two separate faculties. They don't belong to each other. I think it's quite a natural thing that universities in China name the degree as B.Eng. If fact, my grandfather got his B.Eng from 同济 before 1949.
So don't worry about the term "Bachelor of Enigneering" on your notarization document. It's perfectly acceptable:)