The recipient could also be a new character created in the fanfiction. Maybe a wizard who has been secretly working against Harry and his friends. Harry sends the Howler to expose this person and put them on notice that he's aware of their actions and won't let them continue.
It could be Umbridge. After all the horrible things she did at Hogwarts, Harry might send a Howler to her when he has the chance. The Howler would be a great way to get back at her for her cruel punishments and her attempts to undermine Dumbledore and the whole Hogwarts community.
Snape could also be a possibility. If Harry did something that Snape considered a serious offense in Potions class, like using an ingredient in the wrong way that could have caused an explosion, Snape might send a howler to scold him. However, it would probably also be filled with his usual sarcasm and dislike for Harry.
It could be Dumbledore. He was always one to oppose Voldemort and a howler from him would be a very interesting plot point. He might use it to taunt Voldemort or to try and make him second - guess his actions.
It could be Professor Snape. He often had a contentious relationship with Harry, and if Harry did something that Snape thought was particularly wrong or against school rules in a way that affected Snape's interests, he might send a Howler.
The Howler might contain Harry's anger and defiance. He could be yelling about all the harm Voldemort has caused, like the deaths of his parents and many others. It could also include threats of how Harry will stop him once and for all.
It could be one of his professors. If Teddy was constantly late to class or not doing his homework, a strict professor like Professor McGonagall might send a Howler to set him straight.
Well, it could be that Harry sends a Howler to the Ministry of Magic. He might be frustrated with their inaction or wrong decisions regarding the safety of Hogwarts. The Howler could expose some of their secrets or simply be a very public outburst of Harry's dissatisfaction, leading to a big political mess within the wizarding world.
In this fanfiction, perhaps the howler scolds Harry for something he did that he thought was right but others disagreed. Maybe it's about his actions during a Quidditch match that were considered too risky. The howler could be from McGonagall, for example.
His father, Harry Potter, might also send a Howler. Harry knows the importance of discipline and responsibility, and if James was shirking his duties or not following the rules at Hogwarts, Harry would not hesitate to use a Howler to communicate his disappointment and expectations.
It could be that someone did something really wrong and Harry needed to express his strong feelings in a very public and intense way. Howlers are notorious for being attention-grabbing and forceful.
In a fanfiction, the howler could have had a physical form beyond just a shrieking letter. It could be that when it arrived at Hogwarts, it took on the form of Molly herself for a brief moment. She could have given Ron a stern look and a lecture in person (sort of) before disappearing again. This would add a whole new level of drama and magic to the concept of the howler in the Harry Potter universe.