The cultural context can be a factor too. A cologne with ingredients that are native to a particular region might tell a story of that place. For instance, a cologne with oud from the Middle East could tell a story of the rich, exotic culture there. The scent can transport you to that place and give you a sense of its traditions, people, and history.
Well, it could be that Harry is raised in a world where cologne has some sort of magical property. Maybe the scent of a particular cologne is used to protect him or give him special powers. For example, the cologne might be made from rare magical ingredients and whenever Harry wears it, he can blend into the Muggle world more easily because it masks his wizardly aura.
The true story of Cowboy Charlie Siringo is one of adventure and hardship on the Texas range. He faced many challenges but persevered with his cowboy spirit.