It is possible to query for two streets to easily see the place where the two selected streets intersect. (The only way to actually query for an intersection itself would be if there were a map layer containing point objects representing the locations of the street intersections.)
The correct SQL Builder query string to use is:
(name = 'xxx') or (name = 'yyy')
You must use "or". "And" will not work because it is impossible to have two names for a single vector shape, i.e., street line.