The Etruscans had several names in antiquity: the Greeks called them Tyrsenoi or Tyrrhenoi, the Roman Tusci or Etrusci (and their country Etruria). All these names seem to be related, ultimately coming from a root Turs- (or maybe Trus-). (The Etruscans themselves seem to have used a completely different name, Rasenna or Rasna.)
Thus Turs- plus the Greek ethnonymic suffix -en- gives Tyrsenoi (or Tyrrhenoi with the regular change -rs- > -ss-). In Latin, Turs-ci would give Tusci. With metathesis, Turs- becomes Trus-, and this seems to underlie E-trus-ci and E-trur-ia (from E-trus-ia with regular rhotacism). But why the E- in these last two forms?
Adding prothetic e- before a consonant cluster is, of course, something that many languages do, but Latin doesn't. Latin has no problem with words beginning tr-, so there's no reason to add an initial e-. The only hypothesis I can think of is that the Romans got this name through some other, unknown language which didn't allow initial consonant clusters, and the e- is due to that language. This is probably an unanswerable question, but has anyone speculated about this initial e-?