Yes, a person can consider themselves to be a chef even if they have never worked as a professional cook but make great food at home. The title of "chef" generally refers to someone who is skilled in the culinary arts and prepares food at a high level of expertise and creativity.
While formal training and professional experience can certainly contribute to someone being recognized as a chef, they are not the sole determining factors. Many self-taught home cooks develop exceptional culinary skills through practice, experimentation, and a deep passion for cooking. If someone consistently creates delicious and well-executed meals at home, they can certainly consider themselves a chef in their own right, regardless of their professional background.
Ultimately, the title of "chef" is not strictly defined, and it can be self-assumed based on one's personal cooking abilities and accomplishments. It's more about the skill, knowledge, and passion for cooking than the specific setting in which the cooking takes place.