The Human empire is an abstract concept more than a concrete example or accepted proper formal name of any sovereign government. An empire is expansionist in nature with colonies established which do not have significant autonomy over the larger government. Colonies in an empire must yield and defer significant authority to that larger government. The relationship is not symmetric nor in any colony's favor. When the human government is not structured as a unified empire, it is more appropriate to call it "humanity" to simply refer to the combined population and established populations. Alternatively, it could be called the Interstellar human community
When the United Nations held full control over the Sol system, it was effectively the human empire. Once Martians gained independence, neither the distinct sovereign governments held control of a unified empire.
When the Empire of Laconia conquered the powers of the Sol system, they unified humanity into a single human empire. They did not, however, change the name of their own government. Instead, they forced all other governments to adopt the name of the Laconian empire and defer to the authority thereof.