Background: The choices of participants in nephrology research genomics studies about receiving additional findings (AFs) are unclear as are participant factors that might influence those choices. Methods: Participant choices and factors potentially impacting decisions about AFs were examined in an Australian study applying research genomic testing following uninformative diagnostic genetic testing for suspected monogenic kidney disease. Results: 93% of participants (195/210) chose to receive potential AFs. There were no statistically significant differences between those consenting to receive AFs or not in terms of gender (p = 0.97), median age (p = 0.56), being personally affected by the inherited kidney disease of interest (p = 0.38), or by the inheritance pattern (p = 0.12–0.19). Participants were more likely to choose not to receive AFs if the family proband presented in adulthood (p = 0.01), if there was family history of another genetic disorder (p = 0.01), and where the consent process was undertaken by an adult nephrologist (p = 0.01). Conclusion: The majority of participants in this nephrology research genomics study chose to receive potential AFs. Younger age of the family proband, family history of an alternate genetic disorder, and consenting by some multidisciplinary team members might impact upon participant choices.