Background/Objectives: Ketamine/esketamine has a rapid/robust antidepressant effect on treatment-resistant depression (TRD). However, its long-term cognitive effects remain unclear. In this study, we investigated the potential cognitive effects of an esketamine spray on a series of TRD patients. Methods: We evaluated the cognitive performance of eight TRD patients subjected to an esketamine nasal spray as an adjunct treatment for six months. Cognitive assessments were performed before treatment initiation (T0) and at three (T3) and six (T6) months by an experienced neuropsychologist using a comprehensive neuropsychological battery. Depression severity was assessed by the Montgomery–Åsberg Depression Rating Scale. Changes in cognitive performance were analyzed by determining the bias between time points. To investigate the association between the severity of depression and performance on cognitive tests, we used correlation with correction for repeated measures and regression analysis with a general linear mixed model. We used the Tukey method to compare three estimates and the Dunnett method to compare two estimates. Results: Improvements in at least one test from T0 to T6 were found for attention, memory, and the executive functions of working memory, set-shifting, and inhibitory control. Most of the improvements had occurred by T3, but working memory and set-shifting improvements were significant only at T6. The severity of depression decreased significantly from T0 to T6, and most cognitive improvements were correlated with an improvement in depression severity. No test indicated a worsening of cognitive performance from T0 to T6. Conclusions: Our results suggest that the cognitive performance of TRD patients improved with long-term adjunct treatment with an esketamine nasal spray. Confirmatory studies are necessary.