The first order of business is the declaration of the name of the king and his authority through his lineage. This will be followed by Ammon’s declaration of name and lineage in verse 13.
The circumstances of Ammon and his brothers’ arrival at the time the king was outside of the walls of his city created this particular confrontation. Had they arrived at a different time they might have had a very different type of introduction to the city. It would likely have been much more difficult to obtain an audience with the king.
The reason for the caution is the protection of the leader. The modern world continues this tradition. Kings and other leaders are to be protected. The second reason will be part of the unfolding story. At this point, the only thing that is certain is that Ammon and his brothers approached a guarded king, and that, in and of itself, might have been punishable by death.
Fortunately for Ammon and his brothers, king Limhi allows them to explain themselves.