Cole* has suggested the Trannon is one of a number of rivers whose names derive from a British Celtic name/term Trisanton[a]. That the term was used usually relies on Ptolemy (2nd C: see Other Works) who gives the River Trisantonis (though see the discussion by Ikins*), and Tacitus (109 CE), who, in his Annals, gives the more ambiguous detrahere arma suspectis cunctaque castris Avonam et Sabrinam fluvios cohibere parat. This was translated along the lines of "he prepared to disarm all whom he suspected, and to occupy with encampments the whole country to the Avon and Severn" (see, for example here) until Bradley, who suggested it was rather cis Trisantonam which might translate as "this side of the Trisantona" (c.p. our Trans Hannoni: Note). Subsequently, this has usually been taken to refer to the Trent, mainly because it seems likely that during the period in question this would have been a possible limit of the Romans' safe influence.
Cole suggests the term is either derived from the British for "Strong/Great"-"Path/Wanderer/Flooder/Pourer" or the related "road that crosses [a watershed]" (her suggestion). She further suggests that the Tarrant (Sussex Arun), Tarrant (Dorset), Trent (Dorset Piddle), Trent Brook (Dorset), Trentan (Badsey Brook, Worcs), Trent (Northern England) and the Trannon (Powys) (plus, possibly, the Trisanna of Austria) are all derived from this usage. Camden has made the jump from this name to the Wonder (see Note) however, it seems something of a jump from Trans Hannoni to Trisantona and then from there to Tarannon or Traanta/Trent.