Moroni gave his banner a name: “Title of Liberty.” By giving it a name, it could be referenced even if not present, and the name would convey the message of the words even when the words could not be read. Right after introducing the name, Mormon notes that it was associated with Christians, with those who had taken upon themselves the name of Christ.
The first important point is that this is the language of translation, and uses the English words as we have received them. The actual names used would have been more appropriate to the language of the Nephites, yet they would still identify the Nephites as a people who believed in the coming Messiah, whatever those words were.
The next important point is that liberty is not associated with political freedoms, but with a specific religion. For the Nephites, their religion was at the heart of who they were, and at the heart of their politics. The ancient world did not make the divisions between politics and religion that modern peoples take for granted. Thus, the threat to liberty, while begun in the realm of politics, was most directly a threat to religious liberty. In verse 10, Mormon has written: “[Amalickiah sought] to destroy the church of God, and to destroy the foundation of liberty.”
The Nephites had some unique beliefs, and the most important was their acceptance of the coming Messiah. The most common apostate notion was to reject that belief. Therefore, it was understood that the rise of Amalickiah and the desire to return to a king brought with it a change to the religious climate, and probably to the prohibition of the belief of those who called themselves after the name of the coming Messiah.