If there is no separate room designated for cooking and eating in a house, it is common to refer to that area simply as the "kitchen." In many homes, especially smaller or more open-concept living spaces, the kitchen area serves multiple purposes, including cooking, dining, and sometimes even socializing.
In such cases, the kitchen space may be connected to a larger common area that encompasses both the dining and living areas. The terms "dining room" and "living room" are more likely to be used when there are distinct, separate spaces for these activities. However, when the kitchen area is integrated into a larger open space, it is generally referred to as the kitchen, even if it also functions as a dining or living area.