A company's name often personifies the company. In the case of family companies, the name is mainly connected with that of the owning family. This paper aims to identify and substantiate the context of the perception of any possible risks from the association of a family name with that of a family company during the generational exchange with the participation of several generations in the family company's management. The hypotheses have been verified based on the evaluation of data acquired from a sample of 245 respondents from the Czech Republic. The research period is 2017-2019. The qualitative research is based on round discussion tables with family business owners. The data has been processed using correlation and regression analysis. The authors have shown that owners consider the association of the family name with that of a family company to be a potential risk. Any negative regard for the family company and the family could lead to losing the family's good name and the company and losing customers and employees. Moreover, it could damage the process of intergenerational transition. The connection between the intensity of the risk perception and the generational exchange process with the participation of several members in the management of a family company has been statistically demonstrated. The degree of perception of the risk is high in family companies where the generational exchange is still ongoing. The exclusion of the variable of the connection of a family company name with the owning family due to collinearity suggests a possibility for a different type of research that would demonstrate the statistical significance. The unique article nature lies in the fact that it involves research into the current, real process of generational exchange taking place in Czech family companies with mainly two generations and up to three generations in the family company management.