The word Sway popped up for the first time in the U.S. baby name data in 2001:
2003: 14 baby girls and 5 baby boys named Sway
2002: 12 baby girls named Sway
2001: 8 baby girls named Sway [debut]
For a long time I assumed the main influence was MTV personality Sway Calloway. But, while I still think Sway had an influence on male usage, I’ve since discovered a much better explanation for the 2001 debut as a female name.
One of the main characters in the 2000 car heist film Gone in 60 Seconds was mechanic-slash-bartender Sara “Sway” Wayland (played by Angelina Jolie). She was the love interest of protagonist Randall “Memphis” Raines (played by Nicolas Cage), who was tasked with stealing 50 specific, expensive cars inside of 72 hours.
The film didn’t get great reviews, but I do remember appreciating the fact that each of the 50 cars was assigned a feminine code-name: