Both of your names are found in Ireland as the English versions of native Irish surnames. Could they be surnames of ancestors on either your father's or mother's side?
According to MacLysaght, the author of a couple of standard works on Irish surnames, (O') Tynan comes from Ó Teimhneáin. He quotes an older authority, Woulfe, as saying the name comes from Teimhean meaning dark or grey. But MacL has his doubts because he adds that this 'must be accepted with reserve'.
(O') Curran comes from Ó Corráin (or Ó Curráin). MacL doesn't say what the name means and I wouldn't hazard a guess either.