Please be careful! If I'm understanding you correctly, you are thinking about using the concept labels (the labels above the concept) to type McDonalds for the left concept and Burger King for the right concept. We have stern warnings in our software to not put anything in the concept labels that would make a meaningful difference to respondents (you should always use nondescript phrases such as "Concept A" and "Concept B"). That's because we do not estimate alternative specific constants representing the position in the questionnaire.
If you want an alternative-specific design (list of attributes for McDonald's and a different list of attributes for Burger King) then your first attribute should be the restaurant name with levels "McDonald's" and "Burger King". Then, you specify the attributes in the list both for McDonald's and for Burger King, specify the prohibitions to make it happen, and make sure to click the box in the software that tells the designer that this is an alternative-specific design.