When copying a list or a site you will have an extra option before the copy which will allow you to change the Title and Url of the object you are copying.
This is very useful when you want to correct old structure mistakes from the source environment.
This feature can also be used to create a copy of a list on the same site using a different name (i.e. Create an archive list).
By default the fields are populated with the current Title of the object.
When you start a copy of a single list or library the following copy options are accessible. The fields title and url Name allow you to change the destination title and url of the list you are copying.