Naming common odors can be an exceptionally challenging task even for young and healthy individuals. Due to this difficulty, tests of cued odor identification (OID) are used instead of free odor identification in cognitive, neuropsychological, or aging research. Consequently, our understanding of the cognitive demands of free OID is limited. In this study, we analyze the demographic and cognitive factors that influence OID responses of old adults. We utilize a uniquely large dataset (n = 2,479) from a population-based sample of healthy, older Swedish adults (ages 58–102) who participated in free and cued OID using the 16-item Sniffin’ TOM test. The free OID naming responses were categorized as correct, misnamings, or omissions. The results revealed that omissions are surprisingly prevalent, constituting 66.4% of errors and accounting for 87.7% of the age-related differences in task performance. Additionally, we hypothesized that successful free OID would be more closely linked to nonolfactory cognitive abilities, such as verbal fluency, vocabulary, and episodic memory proficiency. This hypothesis was supported, as we found significant associations between free OID and these cognitive abilities, while cued OID identification only was associated with perceptual speed. Our findings suggest that the assessment of free OID may provide valuable insights into odor-based cognition, indicating a need for further research in this area.