Due to the introduction of full names being Western in the other world everyone thinks Kazuya's first name is Souma. He doesn't realize this immense blunder until a few months into being king. He can't fix it.
The first opening only names Souma and those who help with his reforms.
The rebuilding Souma does is mostly through reform policies, effectively "rebuilding from the ground up". There's some actual construction and such, but it largely comes secondary to the more important issues.