It was somewhat surprising that Sony tried to trademark the term "Let's Play", which these days is synonymous with recordings of people playing games, mostly with added commentary. It's these kinds of videos that have proved enduringly popular and through their popularity have helped companies like Twitch grow into what they are today.
It's not clear why Sony tried to trademark the game, and we'll probably never know for sure (unless they tell us, of course), but we do know that the American Patent Office rejected their request.
Why did they reject the trademark application? Well it turns out that the explanation is as surprising as initial the proposal. The reason for the rejection was that "Let's Play" is just too similar to the already trademarked "Let'z Play". Sony can still lodge an appeal against this verdict if they think they have a chance of overturning the decision.