The Thane of Cawdor is not named in Macbeth. But, in Act I, Scene 2, the Thane of Cawdor is labeled a Scottish traitor by the Thane of Ross when he returns to camp. Further, Ross reports that the Norwegians, who have been in "terrible numbers," fought with the king's troops. In fact, the king of Norway himself did battle with the Scots. His soldiers were aided by the Thane of Cawdor, called "the disloyal traitor" by Ross. It has been a "dismal conflict," one that threatens Scotland, in which they all engaged. But, after the mighty Macbeth reached the battlefield, the Scots defeated Norway.

Hearing this report, Scotland's king, Duncan, tells Ross that he wants Macbeth awarded the title Thane of Cawdor because of his bravery and skill. Furthermore, King Duncan orders that the traitorous Thane of Cawdor be put to death and his title awarded to Macbeth for his bravery. "What he hath lost, noble Macbeth hath won" (1.2.68).

We don't actually meet or find out the name of the person who was Thane of Cawdor before Macbeth, because Duncan has him executed pretty quickly as a punishment for his treason.  While Macbeth and Banquo were off fighting the "merciless Macdonwald," who Macbeth "unseam'd from the nave to th' chops," the old Thane of Cawdor had turned on king and country to help the king of Norway invade Scotland.  It makes sense to Duncan to give the title that had been held by a traitor to one of his bravest and most trusted nobles because he would obviously want to install those he feels he can depend on in the positions closest to him.  He also just wants to honor Macbeth for his courageous service to the country.