Orodruin said:
No it wasn't. It was the Anakin/Luke saber. He might consider it "his" and desire it due to his obsession with Vader, but there need not be much more to it than that.
Your theory also does not explain why a large number of people seem to know who Ray is, which you could also reasonably argue is all there in the acting.
Did you miss the part where Ben "That saber belongs to me!" Which according to the novelization he recognized. How else would he have known it was his grandfather's then uncle's old weapon? When Anakin went full on Darth Vader he wasn't using his old saber anymore so it's not like there was a myriad of footage floating around with him using it. In fact most people didn't even know Anakin and Vader were the same person until well after Return of the Jedi and a couple years before the events of The Force Awakens.
Yeah it was Luke's but he built a new saber after he lost his first one. Obviously it was found and it would make sense for him to give his old one to his nephew. It is a family heirloom so giving it to the youngest member of the family who is learning the force would make sense.
Hail when Han saw the saber for the first time it brought out a look of anger and revulsion. And it is easy to ascertain Han did not approve of his son joining Luke's academy and using the force. It is easy to conclude he saw the saber as the first step that sent his boy spiraling to the dark side. If it was just Lukes why would it bring out such strong emotions in Han?
No one in the movie recognized Rey. Not Han; who wanted to dump her and Finn on the nearest inhabited star system the first chance he and Chewie got. If he was her uncle and she was missing all these years why would he let her out of his sight after finding her, by pure happenstance? He didn't even know her name. He had to ask her. And if he did know Rey and her backstory why was he going to let her go back to Jakku and wait for someone who is never coming back? Wouldn't he had told her "Rey I'm your family. I know your dad and my wife Leia is your aunt."
Speaking of Leia she didn't know Rey either. When she was kidnapped by her son she was more concerned with pumping Finn for more information about Star Killer Base than rescuing her supposed "niece." If Rey was related to her saving her would have been priority number one or at least as important as getting information about SKB.
When Kylo captured Rey Han wasn't as concerned as an uncle whose niece was kidnapped, by his own son nonetheless. He blew Finn off to talk to Leia and all they talked about was him seeing Ben. Not once did he throw in "by the way I found Luke's kid." Just small talk and what caused their marriage to fail. They would be horrible relatives to not show any emotion over a long lost family member being abducted.
And Leia never met Rey until after Han died. That was the first time the two ever met. JJ Abraham said so himself. You know who he said never met Rey until TFA, as well? Kylo Ren her supposed cousin. In the movies commentary track the director said Ben and Reys first time meeting was in Takodana Woods when he captured her.
And no Maz didn't know or say Rey is a Skywalker either. The opposite really. "Whoever your waiting for on Jakku is not coming back; The belonging your waiting for lies ahead not behind you." Seeing as how she is spending most of The Last Jedi with Luke and Kylo that eliminates them as the ones who left her behind. The only reason Maz asked who the girl was is because she is force sensitive and sensed Rey was too. The only thing Han told her was the same thing we the audience already knew so there was no point in showing us what he told her. All that moment was meant to do was foreshadow there is something special about Rey.
Lastly Luke's expression at the end of the movie wasn't that of a man who discovered his long lost child. Hail seeing the saber is the only thing that brought out any recognition. His face wasn't that of someone happy to see Rey, at all. Even Daisy Ridley said his face was saying, who are you? What are you doing here and why do you have my old weapon?
. There are a lot of theories out there on the internet/youtube...