"Elena," Brian whispered softly to the woman. The distance that separated them prevented Elena from hearing what Brian was saying. But from the movement of the man's lips, it was implied that her name had been spoken by Brian.
Knowing what Brian said, made Elena think of Elise. Elena realized that she shouldn't have met that man. Brian shouldn't know if she just met Dean. Realizing the current emergency situation, Elena immediately turned around and ran at once.
Elena's action made Brian shout her name, "Elena!"
But Elena didn't stop at all, the woman ran even faster. Without realizing it, Brian ran after Elena. He couldn't just let Elena go.