Cohorts in Mixpanel that are based on user profile properties are dynamic โ they are not static snapshots. However, there's one important thing to note:
Because user profile properties only store the most recent value, cohorts involving user profile properties will use the current value of those properties at the time the cohort is evaluated.
So as new users are added and their profileName property is set, they will automatically be included in the cohort the next time it is evaluated. [Cohorts docs]