Disagree with this if you must, but hear me out. I fully believe that Rey is daughter of Luke Skywalker. There are many reasons that lead me to believe Rey is a Skywalker and here they are.
Q1. She doesn't remember who her actual parents, ever since she was abandoned on Jakku.
A. Luke must have left her there to keep her safe. He was burdened with the fact that his nephew Ben/ Kylo Ren turned to the Dark Side
Q2. Luke's Lightsaber called out to her.
A. Now if she wasn't Luke's daughter, why would Luke's very own Lightsaber call out to her? With her touching her father's Lightsaber, it awakens The Force within her, making it more clear for her to use it later in the movie.
Q3. Kylo Ren seemed weaker against her, though he has been taught longer.
A. In the film, Kylo Ren tries to use The Force to get answers out of Rey, which did not work, because she used The Force to repel his torture. The family ties between the two brought The Force to them both. Kylo Ren has been with The Force longer but he also had his so called "Rage Quits" because he didn't have his emotions in check. Rey's use of The Force came quickly, but she had more control over her emotions faster than her cousin whom she fought against.
Q4. Luke's reaction seeing Rey.
A. Luke has been exiled to an old Jedi Temple, blaming himself for what happened to Ben/ Kylo Ren. When Rey climbs those steps, to finally see Luke, her reaction to him isn't quite same as his to her. Luke knows that she is his daughter, but she doesn't know that yet. The look in Luke's eyes read 'My Daughter has found me.' Even though his face appears to still hold that tortured pained look, he is seeing his daughter standing before him handing him his Lightsaber. Before the screen goes black, just Rey holding out Luke's Lightsaber, tells him silently "train me" and a quick shot back to Luke shows that he agrees.