The scene is not in real time. There would have been plenty of chances for them to introduce themselves. Remember Bill loves to tell everyone that he is a doctor.
It could very well be a clue that it was all a dream/in his head. Take note to where Bill met Domino it was on the same street as Sonata Cafe. Later on the rainbow fashion store is across the street from Sonata Cafe (you can see the reflection in the window). So, geographically it all takes place in a single square block area, possibly just lack of set design, or is it a dream? Also, through the movie he keeps visiting the same location only difference is, what he is visiting should not be where he is. for instance the coffee shop is rainbow fashions, and across the street is sonata cafe and next to sonata is gillespie's cafe (look at the set). Even when he visits Gillespies cafe to ask for nightingale, the rainbow fashion, across the street is under construction. So it all could be a dream,
A mental problem? A hint towards what is communicated in film, which is a realm somewhere between dream and reality? Some real, some unreal - uncanny stuff.