In Macbeth, who is named heir to the Scottish throne?

King Duncan names his eldest son, Malcolm, as heir to his throne. This happens soon after the traitors Macdonwald, the thane of Cawdor, and the Norwegian troops, under the leadership of Sweno, are defeated by the Scottish army. The thanes, generals and other leaders are all gathered at King Duncan's palace in Forres, when he makes the following announcement:

... We will establish our estate upon
Our eldest, Malcolm, whom we name hereafter
The Prince of Cumberland; which honour must
Not unaccompanied invest him only,
But signs of nobleness, like stars, shall shine
On all deservers. From hence to Inverness,
And bind us further to you.

The king has also graciously offered numerous accolades and rewards to various other men, such as Macbeth who had been granted the title thane of Cawdor, for their unwavering defence of king and country. He extends honour and praise to all out of gratitude for their courage and loyalty.

Since Macbeth is now the highest ranking general in Duncan's army and also the king's cousin, Duncan decides that they shall proceed to his castle at Inverness, there to celebrate their victory. The king clearly has much admiration for his cousin and calls him 'worthy.' It is ironic that he has such high regard for him since Macbeth has already started to plot his downfall, so that he may ascend to the throne.

In an aside Macbeth mutters:

The Prince of Cumberland! that is a step
On which I must fall down, or else o'erleap,
For in my way it lies. Stars, hide your fires;
Let not light see my black and deep desires:
The eye wink at the hand; yet let that be,
Which the eye fears, when it is done, to see.

In these lines he clearly states his intent and sees the fact that Malcolm has been named heir as a development which should either lead to his failure of obtaining the crown or which he has to overcome, for it is a hurdle in his quest. In this instance he metaphorically asks that the stars not shine and thus veil his evil plan in darkness.

It is evident in the last two lines that Macbeth has already thought about how he was going to execute Duncan. The eye must not know what the hand is doing when it commits a foul deed. It is as if Macbeth has already seen the dagger with which to murder Duncan, in his hand. However, that should not make him falter or stop, for that which the eye is afraid to see will be done and will be seen to be done. Macbeth is determined to follow through with his plot.