Star Wars, at least the numbered “saga” entries, has been about the Skywalker line. (I’m ignoring all of the EU/Legends stuff since it isn’t relevant post-Disney.)
IV-VI were about Luke Skywalker’s journey to becoming a Jedi Knight, set against the destruction of the Empire.
I-III were about Anakin Skywalker and his fall to the Dark Side, set against the fall of the Old Republic and the rise of the Empire.
In VII, the central character was a young woman without a last name, set against a conflict between a nascent New Republic and the remnants of the Empire. (I also strongly disliked that TLJ defaulted back to the ragtag Rebellion vs Empire conflict from the OT, which makes the notion that Rian Johnson gave the audience something “new” rather laughable.)
Given the history of the saga, it stands to reason that Rey is a Skywalker, and probably Luke’s daughter.
Reducing Rey to just a random person diminshes the saga. It wouldn’t have bothered me if she was just another face in the crowd if this wasn’t “Episode VII,” but the previous two trilogies have set up this pattern, that the Star Wars saga is the story of the Skywalker line. It’s essentially an epic high fantasy with sci-fi trappings. True, Kylo Ren is a Skywalker, but he’s hardly the central or POV character of this trilogy like Anakin and Luke were in their trilogies.
In VII, Rey’s name is a mystery. Daisy Ridley looks like she could be related to Carrie Fisher and Natalie Portman. She’s strong in the Force like Luke and Anakin. She uses the Force like she has at least some training. The lightsaber owned by both Anakin and Luke called out to her. There are enough breadcrumbs scattered throughout TFA to point in this direction.
I wouldn’t object to Rey being random girl if this wasn’t part of the “saga,” and set in the past or far future of the SW universe. I wouldn’t have wanted Jyn Erso to be Han Solo’s cousin in Rogue One, or Hux to be Tarkin’s nephew, or Finn to be Lando’s grandson, but having Rey be Luke’s daughter seems like an obvious and necessary element of the greater saga.