The research explores the definition of the reputation of a higher educational institution (HEI) as an integral concept and evaluates the role of the reputational responsibility of universities in enhancing the competitiveness of the educational institution, influencing its position in domestic and international rankings. The research pays particular attention to the structure of the university's reputation as a multifaceted concept, highlighting Russian and international approaches to shaping reputation as a factor in increasing the university's competitiveness in contemporary conditions. The "Priority 2030" program and the requirements for the reputational profiles of universities participating in this program are examined, considering the digitization of Russian society and education. During the research, the authors propose an original methodology for assessing the reputation of a university based on the key requirements of "Priority 2030," present the results of the testing of this methodology, and provide reputational profiles for three leading Russian universities on which the assessment is conducted. The expert assessment data for the three leading universities in Russia were collected in 2022, considering contemporary trends in digital education development and the requirements of the "Priority 2030" program. The methodology and approach disclosed in this research can enrich the toolkit for assessing the reputation of a university and building a reputational profile. It also complements the criteria and evaluation methods by incorporating digital components, which are currently absent in most classical assessment approaches. The research may be valuable for education administrators, students, graduate students, and anyone interested in the topic of assessing a university's reputational profile with the aim of enhancing its competitiveness in domestic and international rankings. [For the complete volume, "University 4.0 and Educational Technology for Sustainable Development: Best Practices and Perspectives in Russia and Central Asia. Education in the Asia-Pacific Region: Issues, Concerns and Prospects. Volume 75," see ED675741.]