Mantis#1428. Thank you kindly, fdg for a patch that solves:

When you copy an item in inventory and paste it, the name gets lost. 
Also when you use "Save as" in the Appearance Editing window the 
created item in inventory has always the name "New <item-type>", 
regardless of what you typed in as name.

OpenSim/Region/Environment/Scenes/Scene.Inventory.cs

@@ -513,6 +513,11 @@ namespace OpenSim.Region.Environment.Scenes
 
             if (asset != null)
             {
+                if (newName != String.Empty)
+                {
+                    asset.Name = newName;
+                }
+
                 if (remoteClient.AgentId == oldAgentID)
                 {
                     CreateNewInventoryItem(