Cohort commander?

[Frank]

These are both auxiliary cohorts?

Both use names in genitive, so in Greek Φ̣λ̣α̣ο̣υ̣ί̣α̣ς̣ really means OF Flavia. I thought they would mean of legion Flavia but as I realize now they are just names for the cohorts instead of the legion they may belong to? And the number just means that there were more auxiliary cohorts of these names? So every time we see something in the format

cohort xx of name

it is always an auxiliary cohort?

Yes, Cohors I Flavia just means, that this unit was founded by a Flavian emperor (Vespasian, Titus, Domitian). Sometimes it could mean, that some famous Flavius was a commander of this cohort. But that seems not to be the case here. There is also a Legio IV Flavia Felix and a Legio XVI Flavia Firma. These names behind the number are just titles (Felix) and/or honoring the empire (Flavia). Without the explicit mention of Legio(nis), it is never a legion.

If so, then, do we have examples of any cohorts actually belonging to legions in epigraphy? I couldn't find a single example for that which is kind of strange. Even ekatontarchs (centurions) linked with legions are always plainly called "ekatontarchs of Legion X" but they surely were not freely assignable to any legionary sub-division.... They seem to be treated exactly like the chiliarchs in epigraphy.

All staff members of a legion (tribuni, praefectus castrorum, etc.) usually just name their legion, because they worked for the legion and did not command a single cohort or belonged to a cohors de facto.

Centurions sometimes used their full titel, which includes the cohors, e.g. centurio decimus hastatus posterior legionis X. Decimus means the 10th Cohort. And even the pilus prior, who was the highest ranked centurio of a legionary cohort, just said soemthing like Centurio pilus prior cohortis III legionis X, or Tertius pilus prior legionis X, which unfortunately means nothing according to leadership.

This is exactly the issue we are discussing in this thread. There was never mentioned a permanent commander of a legionary cohort! No tribunes, no praefects and no centurions. Just commanders of auxilia cohorts or temporary vexillationes. Such a vexillatio leaded by a tribunus legionis or a centurio could be exact 1 legionary cohort. But again, this means nothing about regulary, permanent command of legionary cohorts, if the cohors is acting together with the other 9 cohorts of the legion in camp or on the battlefield.