I will not out right deny a family link, but Luke conquered the temptation to join the dark side in Return of the Jedi. There is no motivation from where I sit that suggests he would turn. I can come up with a few ideas to explain Ren. My favorite is that he is Luke's son who he tried to train but he turned, being tempted by the dark side and feeling that he must carry out Granddaddy Vader's legacy. Ren could have killed his mother (Luke's wife/lover) to complete his turn. Luke, overcome with guilt over his failure to train his own son, goes into hiding.

The order Kylo is a part of, the "Knights of Ren", see the Empire as heroes, ave Darth Vader as martyr. It's like how churches covet "holy relics"

Because he is a fan boy?

Because darth vader was the bad b*tch on campus