After read about Ship of Theseus paradox I was in a big doubt, I looked in Wikipedia, Google, but I can't found an unique mention of this issue: does his ship have its own name?
The ship has no name. This story came to us from Plutarch, who writes that:
The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.
This ships is identified as the one that Ancient Athens used to send to Delos to honour Apollo. That story is preserved by Plato, who explains:
The stern of the ship which the Athenians sent to Delos happened to have been crowned on the day before he was tried ... It is the ship in which, according to Athenian tradition, Theseus went to Crete when he took with him the fourteen youths, and was the saviour of them and of himself. And they are said to have vowed to Apollo at the time, that if they were saved they would send a yearly mission to Delos. Now this custom still continues, and the whole period of the voyage to and from Delos, beginning when the priest of Apollo crowns the stern of the ship, is a holy season.
No name has been attributed to the ship in either account. Thus, the closest thing to a name for the ship is "Theseus' Ship" or "Ship of Theseus".