The title of the play that this film was based on was Sabrina Fair, indicating that the central character of the play, Sabrina, was pretty (or fair).
Hollywood was worried that Sabrina Fair would sound too archaic or fusty though—they also thought it would make people think of the Victorian novel by William Makepeace Thackeray, Vanity Fair.
Basically, Hollywood thought that audiences would run in the other direction from a film that sounded like a fairy tale or a doorstop of an 18th Century novel. And hey: they're probably right. If Mad Max: Fury Road had been called Sir Maximilian Madness: Avenue of Wrath, we probably wouldn't have seen it fifteen times.
So the title of Sabrina is just… Sabrina. That's fairly straightforward; the main character is Sabrina. Almost every scene includes a hefty helping of Sabrina goodness. Sabrina wears all the awesome Givenchy costumes.
Still, you can see the title from a couple slightly different perspectives. Sabrina tells you that the film is Sabrina's story; it's about what happens to her and how she falls in love (just like Cinderella is about Cinderella).
But you could also see the title from Linus and David's perspective; Sabrina enters their lives and changes everything. Sabrina gets corporate grey drone Linus to toss aside his umbrella and go to Paris, land of life and love. She also (indirectly) causes David to set aside his partyboy, manchild shtick and become a responsible adult.