I have no doubt that Greta Thunberg is frequently impersonated (as most celebrities now are). Therefore, seeking trade mark protection for Greta Thunberg, #FridaysForFuture, Skolstrejk för klimatet (school strike for climate) etc is a sensible move to make. By registering these marks, Greta will be in a much better position to take action against said impersonators.
However, Greta may have missed out by only seeking protection for services. If she had sought protection for goods also, clothing for example, she could have licenced use of the marks as another avenue stream for her climate change activism.
Climate change activist Greta Thunberg says she is trademarking her name and the #FridaysForFuture movement to stop people from impersonating her.