There's not enough information to say exactly who Beckett is. It could be a random person with that name who has had an impact on fanfic. Maybe it's a pen name or an alias of someone within the fanfic community or someone who has some sort of authority over the works that fanfic is based on.
Well, in 'larry the scary story', Larry might be a character that is central to the horror elements. Maybe he is a victim, or perhaps he is the source of the scariness. For example, he could be a haunted figure or someone who has stumbled upon a dark secret, which then leads to all the terrifying events in the story.
Larry could be a relatable character in the story. He might be an ordinary person with ordinary dreams, but his need for a friend is what sets the story in motion. Maybe he has a kind heart and is just waiting for someone to notice him and become his friend. He could be of any age, but the common thread is his longing for friendship.
Since we don't have much information given, Larry in '600 lb life larry's story' is presumably an individual who has reached a weight of 600 lbs. He might be from anywhere, with different life circumstances that led to his extreme weight. He's on this show to document his journey of transformation. It could be that he has faced discrimination or has been unable to do things he loves because of his weight. His identity as Larry is tied to his story of facing the challenges of obesity and trying to overcome them with the help of the resources provided by the '600 lb life' program.
I don't know who St Jude Beckett is in this story as I haven't heard of it before. It could be a fictional character or a real person that only a small group of people are familiar with.
It's possible that Beckett and Josh are characters in a fantasy - themed fanfic. Beckett could be a wizard in training and Josh a brave knight. They secretly meet because there are dark forces in the kingdom that would not approve of their alliance. Their meetings are crucial for sharing knowledge and planning strategies to save the kingdom from impending doom.
I'm not certain who Larry Novak is without more context. He could be the author who created this original Christmas story, or perhaps a character within the story itself.