Your libraries have a display name and an internal name in SharePoint. The internal name is what you will find in your URL and the display name is what you will see as the title of your library in SharePoint.
Symptoms
You migrate a site with the team site template to find that the URL of the Documents library changed from /Documents to /Shared Documents at the destination.
Details
When the app migrates your sites, it recreates them from scratch at your migration destination. The new site will have a Documents library that has the default name Shared Documents. Since the tool merges document libraries based on their URLs, which is a reflection of their internal names, your Documents library is automatically merged into the Shared Documents library.
Solution
Create a new site at your migration destination.
Create a library with the same internal name and display name as your source Documents library.
Merge the source site into this new site using copy structure.