Presbyter Adeodatus here is most probably the same as the addressee of other Ennodius's letters, see PCBE, Italie, v. 1, Adeodatus 8. It is possibly also the same person as the Presbyter Adeodatus present at the council of Rome in AD 495  and the Presbyter Adeodatus present at the council in Rome in AD 502 (PCBE Italie, v. 1, Adeodatus 7, 9). It is impossible to say with precision whether we have here one, two, or three different Adeodati.
The poem mentioned in the letter is the epitaph of Cynegia which Ennodius had sent to Adeodatus in his previous letter . Ennodius has sent the poem also to Beatus (see PCBE Italie, v. 1, Beatus 2), his pupil in Rome (Letter VII, 29=Vogel no. 362). In Letter VIII, 29 Ennodius accused Beatus of criticizing the poem. Later, however, after receiving Beatus's response Ennodius apologized for believing rumours (Letter VIII, 21 = Vogel, no. 398).