"Scarlet" (with one T) is the name for a bright shade of red, so I tend to think of that first. The next thing I think of is the character "Scarlett O'Hara," from the book and movie, "Gone with the Wind." Probably younger people would think of the actress Scarlett Johansson.
Scarlet is an intense, bright color, and both Scarlett O'Hara and Scarlett Johansson are, I think, associated with the idea of strong, bold personalities.
I believe it is becoming a popular name, possibly because of Scarlett Johansson.
(Checking) It is now the twentieth most common name given to girls in the United States. That is definitely a new trend. It used to be quite rare.