In the Revit interface, it is possible to rename a Revit Link instance.
In the API, when assiging a string to RevitLinkInstance.Name, we receive a "This element doesn't support assignment of a user-specified name".
PLease note that Revit Lookup reports the RevitLinkInstance.Name as a string following the schema below:
Revit File Name.rvt : Link Instance Name : location <Location>