Which battle features at the start of the play, Macbeth? Is the battle even named?

The battle is not given a specific title, but it is clear from the text that it was part of King Duncan's fight against the rebellious Macdonwald, who had turned against his king, most probably in an attempt to usurp the Scottish throne and claim it for himself.

To this end, Macdonwald has gathered around him a number of allies, such as the thane of Cawdor and Sweno, the king of Norway, who have obviously provided him with men to boost his forces. It is clear from the injured sergeant's report in Act 1 scene 2, that the battle had been fierce and advantage had probably swayed from one party to the other throughout. It becomes evident, though, that it was Macbeth's stubborn resilience and determination which encouraged the king's exhausted troops and ensured victory. The sergeant, in glowing terms, reports in part:

...For brave Macbeth--well he deserves that name--
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,
Like valour's minion carved out his passage
Till he faced the slave;
Which ne'er shook hands, nor bade farewell to him,
Till he unseam'd him from the nave to the chaps,
And fix'd his head upon our battlements.

It was Macbeth's undaunted spirit and valor which won them the day. He confronted the fierce and fiery Macdonwald, showing no courtesy, and executed him, ripping him apart from his navel to his jaw. He then decapitated the traitor and attached his head to the battlements for all to see.

This victory, however, did not scare off the Norwegian king and his troops, for they believed that they had the upper hand and, with new weapons and fresh men, launched a renewed assault. Their inspired action, though, did not dishearten Macbeth and Banquo but, instead, encouraged them, for they doubled their attack.

Ross, on returning from the battlefield, later confirms what the sergeant had reported and states that the king of Norway and the thane of Cawdor were defeated by the force of their fighting. This news obviously provides Duncan much joy for the threat to his crown has been ruthlessly suppressed. In his bliss, he praises Macbeth specifically and, in his absence, awards him the title thane of Cawdor, for the previous thane would be executed for his betrayal. Duncan tells Ross:

No more that thane of Cawdor shall deceive
Our bosom interest: go pronounce his present death,
And with his former title greet Macbeth.

Great irony lies in the fact that firstly, great honour and title is bestowed upon Macbeth for his courage in defending his king and country and secondly, that he had fought against the traitors who wished to overthrow his king. The irony lies in the fact that he betrays the king himself by doing the very thing Macdonwald, Cawdor and Sweno had failed to achieve. He murders the king in his bed later and claims the throne when Duncan's sons escape, fearing for their lives.