"Name" is here not used in the sense of "proper name" but in the sense of "distinguished or honourable repute, honour" (C. T. Onions: A Shakespeare Glossary).
In other words, the Sergeant is saying that Macbeth deserves being called "brave". His own report of the battles explains why.
In all six editions of Macbeth that I have read so far, I don't recall any discussion on the meaning of the name Macbeth. It is a name that Shakespeare found in his main source for the play, Holinshed's Chronicles, and the name of a historical king of Scotland (Macbethad mac Findláech). Kenneth Muir's edition of the play does not discuss the origin of Macbeth' name, nor is this discussed in the appendices, which contain passages from sources that we know Shakespeare used (especially Holinshed) or that he may have used (Buchanan's Rerum Scoticorum Historia and John Leslie's De Origine, Moribus, et Rebus Gestis Scotorum).
Alex Woolf's From Pictland to Alba, 789–1070 tells us that Macbethad was a member of the Moray dynasty (page 229), that he may have spent some time in exile after his father had been killed in 1020 (page 247) and summarises his reign (pages 255–265) but doesn't say anything about the meaning of his name.
However, Benjamin Hudson's Macbeth before Shakespeare briefly discusses Macbeth's name (page 44):
The correct Gaelic form of Macbeth's name is Mac bethad, a compound of two elements: mac (son) and bethad (life). By extension a "Son of Life" meant Christian. (…) During his lifetime the name Mac bethad began the process of contracting into the more familiar form Macbeth.
However, for "name" in the Sergeant's speech to refer to Macbeth's name ("Son of Life"), both Shakespeare and his audience would have needed to be aware of its Gaelic etymology. If Shakespeare had intended this, it would have added some irony, since Macbeth kills so many people.
Sources
- Hudson, Benjamin: Macbeth before Shakespeare. Oxford University Press, 2023.
- Shakespeare, William: Macbeth. Edited by Kenneth Muir. The Arden Shakespeare. London: Routledge, 1984. (The 1984 edition differs from the 1962 edition by a new introduction, new appendices and various other changes.)
- Woolf, Alex: From Pictland to Alba, 789–1070. The New Edinburgh History of Scotland, volume 2. Edinburgh University Press, 2007.