The fact that the name was put between brackets generally means that Settipani did not find a documented name for this person and assumes the person must have had the name that he put between brackets. You will see this practised by other authors as well, not only with brackets but also with square brackets. The brackets for me indicate to be very careful, because it is an assumption and not a documented fact.
In this particular case, as Peter already stated, "Anicia" should be seen as the Roman variant of a surname: Anicia was used for all women of the Roman "gens" Anicius.
If you look at the table on page 292, you see for example 3 generations of (M. Ceionius). This should be read as: Marcus Ceionius Varus, Roman praefectus in 271, in Settipani's opinion was a second great-grandson of Marcus Ceionius Silvanus, Roman consul in 156, and the only thing that can be assumed of the 3 generations between these two persons is that their name probably will have been Marcus Ceionius (Ceionius for sure because it was the name of the gens, Marcus probably because the Roman patricians had the habit of giving their eldest son the same first name as they had themselves), possibly followed by one or more additional names which are not known.
Willem Nabuurs