He gives it to Malcolm.
his son, Malcolm
Malcolm's title is Prince of Cumberland. He is named Duncan's heir apparent. At the time, the eldest son was NOT automatically the next in line for the throne. Macbeth, as the most experienced and respected soldier, expects to be named, but Duncan passes him over for the feckless Malcolm.
Duncan declares his son, Malcolm, to be Prince of Cumberland, which means that he is the heir to the throne. This proclamation tells the audience that in order for Macbeth to become King, not only does he have to murder Duncan but Malcolm too.
King Duncan's full name is Duncan I of Scotland.
Rodney Duncan's birth name is Duncan, Rodney.
Duncan Clyde's birth name is Duncan Watkinson.
Duncan Sheik's birth name is Sheik, Duncan Scott.
Duncan Staff's birth name is Duncan Dennier Staff.
Duncan Regehr's birth name is Duncan Peter Regehr.
Duncan Bannatyne's birth name is Duncan Walker Bannatyne.
Duncan Preston's birth name is Duncan J. Preston.
Duncan McAllister's birth name is Duncan James McAllister.