Every known name of the Celtic tribes, at least in Brittania, seems to be Romanized: Brigantes, Demetae, Iceni, for example. Does removing the Romanized suffix reverse this? Brigant, Demet, Icen..... ? Surely these suffixes, part of a language far-removed from that of pre Roman Britain, didn't apply to these tribes before the invasions of Caesar and Claudius, did they?
No, removing the inflectional endings tells us nothing. For one thing we have very few texts in any Celtic language so that tells us very little. More importantly, the Celtic languages and the Italic languages such as Latin all were Indo-European languages, which hardly makes Celtic "far-removed" from pre-Roman Britain. Actually Celtic was quite closely related to Latin, Oscan, Umbrian, and the rest of the Italic family--so much so that at one time it was suggested that Celtic and Italic descended from the same cultural family which might have settled an area just north of the Alps, speaking "Italo-Celtic" (an idea not taken seriously on the basis of archaeological evidence mostly). In particular, the inflectional endings in most Celtic languages and the pattern of case usage resembled Latin, particularly Archaic Latin, very closely. So Latinate adaptations would hardly have differed much in their use of inflection--in fact they were significantly better than Anglicizations of those names would have been, since most Celtic languages used the same basic declensional endings as Latin, with slightly different pronunciation (although even this, in Archaic Latin, would have been much closer). Furthermore, Latin was quite well known for picking up Celtic words--almost every type of wheeled vehicle in Latin is either borrowed from Celtic or descends directly from the same route as a Celtic word--and was quite well adapted to modify Celtic languages
Now, as for Pictish, which seems to have been something of a mix of Celtic and pre-Celtic speech, it's more difficult to say. We only have a handful of national names in Pictish, however, and a few examples of late Pictish which indicates that the language had inflection similar to that of Celtic languages, probably adopted from them. In any case from what we can tell it seems likely that to the extent that the Romans actually did discriminate between different Pictish tribes (a degree which we are very unsure about) they mainly adopted the Celtic words for those tribes
I'm not sure what you mean by reversed?