... Caractacus is said to express the ability of its first bearer in conducting an offensive as well as a defensive war, and has been derived from Gaelic caer a castle, eacht an exploit, and cios a tribute.  O'Connor derives the name from cathreachtac-eis, the head of the host in battle.  It comes rather from Welsh caraddwg, abounding in love... (Prænomina, Charnock, 1882)

Caractacus.  Attempts have been made by various persons to give the correct etymology of this name; but in every case, as far as I am aware, without success.  O'Connor, in his Chronicles of Eri (vol. i, p. 321), assuming the Gaelic dialect, has it Cath-reacteac-eis, i.e., "the leader and director of the host in battle."  This alters the first syllable, and displays too much circumlocution.  The better derivation will be Caer-vraight-tagos; in English, "the fortress royal commander," or more literally, "king-commander."  This appears to agree sufficiently with the occurrence of the name on coins in the forms Caeratic, Cearatic, and Keratik, as also with his name Arviragus, as in the ancient British Chronicles; the obvious etymology of which is Ard-vraight, or "high king."  The original form of the name, I have supposed, Caer-vraight-tagos, would have had pretty much the same force and import as the title Præfectus Prætorio, or the "Prefect of the Pretorium," which was common at Rome in the time of the emperors; and the opinion may be entertained that Cunobeline had made Caractacus, in the insurrection of Adminius his commander-in-chief and military governor of Camulodunum.  Caractacus' other name, as in the Chronicles, was Gueirydd, or literally, the "administrator of justice." (Celtic Inscriptions on Gaulish & British Coins, Poste, 1861)